Drowning versus Aquatic Distress by Crunderwood

So inspired by my near drowning this morning and subsequent discharge from hospital, I present to you all…

Drowning versus Aquatic Distress


Why Drowning doesn’t look like “Drowning”

Also the science of drowning

Picture this scene: you are standing at the side of a swimming pool and in front of you there are two people in the water. The first is a lady, calling for help, thrashing her arms above her head in visible distress; she needs help and she wants you to come and save her.

The second is another lady; she appears much calmer than the first, her arms are out laterally, pressing down on the water in order to keep afloat. She isn’t calling for help.

Did you realise the second lady only has between 20 and 60 seconds left afloat before she sinks below the surface? She is drowning.

So why does she not meet your expectations of drowning? Well the answer can be summed up in 1 simple word: Television. Due to innumerable television shows and films in which people “drown”, many people are able to recognise the signs of aquatic distress, however they misattribute them to drowning.

So what are the visual clues to drowning?

People who are drowning undergo a physiological response called the Instinctive Drowning Response. There are five main things to look out for in a potential drowning victim:

1. “Except in rare circumstances, drowning people are physiologically unable to call out for help. The respiratory system was designed for breathing. Speech is the secondary or overlaid function. Breathing must be fulfilled before speech occurs.

2. Drowning people’s mouths alternately sink below and reappear above the surface of the water. The mouths of drowning people are not above the surface of the water long enough for them to exhale, inhale, and call out for help. When the drowning people’s mouths are above the surface, they exhale and inhale quickly as their mouths start to sink below the surface of the water.

3. Drowning people cannot wave for help. Nature instinctively forces them to extend their arms laterally and press down on the water’s surface. Pressing down on the surface of the water permits drowning people to leverage their bodies so they can lift their mouths out of the water to breathe.

4. Throughout the Instinctive Drowning Response, drowning people cannot voluntarily control their arm movements. Physiologically, drowning people who are struggling on the surface of the water cannot stop drowning and perform voluntary movements such as waving for help, moving toward a rescuer, or reaching out for a piece of rescue equipment.

5. From beginning to end of the Instinctive Drowning Response people’s bodies remain upright in the water, with no evidence of a supporting kick. Unless rescued by a trained lifeguard, these drowning people can only struggle on the surface of the water from 20 to 60 seconds before submersion occurs.”

So what, then, is Aquatic Distress?

Simply put, aquatic distress is when a person who is not drowning who requires help. They have the mental capacity to realise this and the lung capacity to call for help. One obvious difference between an Aquatic Distress victim and a Drowning victim lies with the ability to help save themselves:
Someone who is experiences Aquatic Distress is able to grab onto ropes, lifebelts and ladders whereas a drowning victim cannot.

The Science of Drowning

As the airways begin to be covered in water, the normal person hold their breath. There is, however, only so long you can hold your breath for before you experience oxygen deprivation: if you are in distress (as you would be) this may be only 30 seconds from when you start holding your breath. Your need for oxygen overrules your conscious knowledge of the water and you start to gasp. You are now drowning.

Your head bobs up and down; covering and uncovering your mouth, however you do not have sufficient time to exhale the water, inhale air then call out before your head drops again. You are aware of your distress however once your lungs have completely exhaled all air, it becomes quite relaxing; like normal breathing however with slightly more resistance.

If your lungs fill with salt water and you are rescued, as long as the water is expelled in sufficient time, you will not generally suffer any long term effects. This is due to the concentration difference between your cells and the saltwater preventing water entering your system. Out with sufficient time, your blood begins to lose water through osmosis, your blood becomes thicker and, once thick enough, can lead to cardiac arrest within 8 minutes.

Freshwater, however, is much more serious. Due to the relatively low concentrations of water in your lung cells, water floods into them the moment it is inside your lungs, rupturing the tissues of the lungs. If the water is expelled, your lungs could then fill with blood resulting in secondary drowning. Water also enters your bloodstream through the exposed capillaries within the lungs. Blood cells begin to burst, upsetting the ion balance. Ventricular fibrillation begins to occur and cardiac arrest follows a mere 22 minutes water. Even if you survive the first few minutes of a fresh water Drowning, you could experience acute renal failure due to the high levels of iron in your blood due to burst blood cells.

Why did I experience near drowning?

We now can include Aquatic Distress into our story about drowning. If you are like me and suffer panic attacks, you may notice that you start to hyperventilate when you have one. Your legs may feel weak and unable to support you. I was standing in the shallow end of a swimming pool with the water barely up to my waist when I had a panic attack. My legs gave out and I began hyperventilating and continued to do so once my mouth went below the surface. Cue drowning. Fortunately, lifeguards at swimming pools are trained to recognise the signs of drowning and were on hand to jump in and pull me out.

What more is there left to say?

If you plan on drowning, aim for saltwater

US Coast Guard “On Scene” Magazine (Autumn 2006)
Instinctive Drowning Response, Mario Vittone (May 2010, July 2011)
American Heart Association Guidelines (2010, part 12)

Overview of Biomimicry by JackTsuchiyama

Overview of Biomimicry

Biomimicry is the design and production of materials, structures, and systems that are modeled on biological entities and processes. Basically, it’s a scientific field that uses biological systems to solve humanity’s industrial problems.

One example is that shark skin has been found to prevent biofilm formation, so Sharklet Technologies has developed a catheter with a micropattern similar to the surface of shark skin. It has been found to reduce microbial growth significantly.

Sandcastle Worms secrete a chemical to create a mineral shell made out of sand; the pH level in the ocean triggers the glue to harden. Scientists have mimicked this secretion to form a synthetic glue which is liquid at room temperature and solid at body temperature. It has been shown to be non-toxic and biodegradable and can be used on complex fractures in the skull, face, knee, ankle, and other joints.

Researchers at Kansai University (関西大学) investigated the micropattern of mosquito needles because they are painful upon penetration. They are now designing a needle that penetrates similarly by creating structures at the nanoscale. It uses pressure to stabilize and painlessly glide into the skin. Current tests have shown that it work flawlessly.

Other applications including modeling air conditioning after termite mounds (Architecture), modeling wind turbine blades after aerodynamic humpback whale fins, modeling solar panels after butterfly wings, using natural ecosystems to develop self-sustaining farms, and modeling communications after dolphins so that signals can be sent underwater.

Biomimicry is becoming more  popular in industry and offers innovative and sustainable challenges in the industrial world. I’m curious to see what else we can pull from nature.

“Definition of Biomimicry.”
The Economist. “Glues bones” (25 Aug 2009).
Rogers, Mike. “What is a Shark?”
“Superglue for Broken Bones” (5 Jun 2012).
The Biomimicry Institute. “Inspiring Sustainable Innovation” (2015).
“Understanding Sharklet Surface Protection Productions” (Apr 2012).

Sexual Indifference by JackTsuchiyama

As all users of the internet know, public opinions and persuasions easily change, and the youth of one year are completely different from the youth of another. This is true in all countries; in Japan it is no different.

Current trends of Japanese 18 year olds:

Pictorial versus verbal communication
Deepening intimacy or dependence on parents
Sexual counter-revolution

Perhaps the lack of sexual interest is due to the pictorial communication style and the dependence upon parents. After all, by the 1980s there was no longer generational gaps and fights between parents and children. However, this intimacy seems to have gone even further in the recent years.

Teenagers comfortably bathe with their parents without an sense of embarassment or any sort of sexuality involved; it’s completely familial bonds and closeness. There are even apps and programs that allow parents to follow their children throughout the day, even at college, and the majority of youths don’t seem bothered by it.

A survey by Rakuten O-net marriage brokerage asked single men & women if they’d want a partner; the results are now around 63-64% which has significantly decreased from the 90% response in 2000.

A statement by a 33-year-old trading company employer in the 1998 Spa! article of “If we love each other, what do we need sex for?” seems to ring true in the current generation. In fact, it’s far more typical that instead of promiscuity, one is to receive the response of “面倒くさい” from them.

Is this unhealthy? Is this troublesome? Or is this the way of the future? I suppose only time will tell.

Hoffman, Michael. “From sexual liberation to liberation from sex” (16 Jan 2016). Available

“Toyama study” by JackTsuchiyama

A study launched in 1989 has found that there’s a correlation between lack of sleep in children and obesity risks as a child and into adulthood. The study targeted ~10,000 babies born that year. These children were assessed every 3 years until they became high school students.

“[M]ore children who had less than nine hours of sleep when they were 3 years old, compared with those who had more than 10 hours, became obese when they reach junior high and high school.” On average, the obesity rate was 1.6 times higher for those with less sleep as a baby.

Obesity in children believed to be caused by lack of exercise and an enriched diet amongst other factors. However, this study indicates that “sleep deficiency in young children is linked to them becoming obese even if lack of exercise as a primary factor is excluded.”

Sleep greatly affects the development of a child’s mind, body, and health. Primarily this is through growth hormones and autonomic nerves. It must be remembered, however, that there are many other factors leading to obesity.

In Japan, only about 3% of children were obese in the 1970s, but since the 1990s this has risen to over 10%.

Therefore, I conclude, you should let your children sleep as much as possible and should make sure they get enough sleep. While this is focusing on children, I also firmly believe that sleep is important throughout your whole life. If only we could all get a little more of it!

Kyodo News. “Researchers link lack of sleep with obesity in children” (22 Jan 2008). Available

Comment: Darn, I didn’t realize this was an older article until just now… Thanks Japan Times.

Effect of Hydrofoils and Canting Masts on Single Handed Sailing Catamarans by Crunderwood

Part one: a short description of Hydrofoils

Hydrofoils are essentially “water wings” – surfaces which produce lift submerged below the waterline resulting in the vessel being lifted from the water. Due to the relative density of water to air being 0.9982 kg/m^3 for fresh water, a hydrofoil can be up to 1000 times smaller than an aerofoil which produces the same amount of lift. Equally, a hydrofoil does not require the same velocity as an aerofoil to produce significant lift.
A great benefit of hydrofoils is the ability to “foil” upwind. The vast majority of high performance racing yachts have a wide beam with a relatively flat underside of the hull. This increases the potential for speed off the wind as the yacht is able to increase her effective waterline length. As the yacht starts to plane, her waterline length increases by 15%, which allows the yacht’s speed to increase. As the speed increases, the effective water line increases, thereby allowing the yacht to increase in speed exponentially (as long as the wind velocity provides the required power).
For a hydrofoil, however, the yacht lifts above the water at a speed much lower than her planing velocity. As she rises, her waterline length drops dramatically – for some yachts dropping by 98% – which according to speed-length equations should dramatically decrease in speed. This is not the case however as the skin friction also drops by equally large percentages – for an AC72, the drop in skin friction could be as high as 86%.
With enough power in the sails to produce a speed high enough to foil, a drop in skin friction on over 40% is enough to overcome hull speed, and once above hull speed, the unfavourable amplification of wave height due to constructive interference diminishes as speed increases.

Part two: Mast cant

Among the vast majority of racing yacht classes, canting the mast is forbidden according to the rules, however, there exists sufficient classes where mast cant is not specifically forbidden which allows for this to be considered.
Cant masts have great advantages over regular masts, for one the mast can be canted to windward, thereby increasing the apparent sail area. As the boat heels, normal masts become less efficient and induce drag and stress by trying to force the boat under the water due to the pressure created by the air flowing over the top of the sail. Cant masts keep the sail closer to vertical, increasing efficiency and reducing the down force on the hull. They can also increase efficiency by canting the sail to windward, this increases the apparent sail area, to more than the static sail area. When the mast is canted to windward it also decreases drag by lifting the hull instead of forcing it down. It works just like a windsurfer does, in fact windsurfers use cant masts and they have been around for a long time.

Part three: Single handed sailing Catamarans

The vessel being considered is an A Class Catamaran. “About the A-Class
A-Class catamarans are the fastest single handed racing boats in the world.
Most other racing classes are one-design whereas the A-Class is a development class and as a result it has become a pure high-tech boat.” As a development class, the A Class Catamaran allows for innovation within the class rules, meaning that hydrofoils and canting masts would be acceptable.

Part four: Application of concepts

Due to recent innovations in class construction, hydrofoils are regularly seen at championship events with several receiving high placings at the 2014 world championships. Speaking with several helmsmen of these boats, the set-up of the foils was relatively similar; the T-foil on the rudder was controlled using a twist rod system in the tiller, and the forward foils were raised and lowered as a standard daggerboard. Fore and aft rake of the forward foil was controlled by a system of blocks set up behind the foil on the topsides, allowing for the foil to be raked upwards (water pressure from forward motion results in raking downwards of the foil).
The canting mast system, however, is yet to be introduced to single handed sailing. This is due to the increase in thought process that even simple manoeuvres would require. For example, consider putting a foiling A Class through a tack:
1.       Drop leeward foil
2.       Rake foils to identical pitch
3.       As you steer into the wind, pull in the mainsail.
4.       Shift weight to centre of the boat whilst controlling the turn
5.       Steer slightly off the wind to heel boat slightly, release mainsail slightly
6.       Shift weight outboard to bring boat upright whilst raising old foil
7.       Pull hard in on mainsail, whilst bringing weight down horizontally.

This manoeuvre takes around three seconds for the highest ranked sailors. Now consider a canting mast being involved:
1.       Drop leeward foil
2.       Rake foils to identical pitch
3.       As you steer into the wind, pull in the mainsail.
4.       Shift weight to centre of the boat whilst controlling the turn, also release mast can to vertical
5.       Steer slightly off the wind to heel boat slightly, release mainsail slightly
6.       Shift weight outboard to bring boat upright whilst raising old foil, also cant mast to new windward
7.       Pull hard in on mainsail, whilst bringing weight down horizontally, finish canting mast to windward

Whilst only a few words long, the increase in effort results in greater energy expenditure, especially aboard an A Class where all work is manual (energy saved by use of mechanical devices is not worth the added weight).

Part five: Effect on Vessel

The largest perceived benefit of a canting mast and hydrofoils is the decrease in required speed to foil. This is due to lift provided by canting the rig to windward as the vessel remains relatively flat. This would increase the speed potential in light wind conditions, providing a great advantage over other foiling catamarans in these conditions. Similarly, the ability to cant the mast to leeward in heavy wind conditions provides the benefit of capsize prevention.
The largest perceived disadvantage of a canting mast and hydrofoils is energy expenditure during race conditions. I one round of a world championship race, competitors can expect to tack over 40 times. Increasing energy usage by a significant amount requires a way to restore energy reserves mid race, adding one more item for the sailor to worry about.


Despite there being a large number of perceived benefits and disadvantages, no concrete conclusion can be drawn without further research. This means that no effect can be guaranteed until such a setup has been trialed at a world championship event.


For further information concerning A Class Catamarans
For further information concerning Hydrofoils
For further information concerning Canting Masts – Not used for original thesis

The majority of information from the original thesis came from the libraries of the University of Strathclyde, Seattle University and MIT.
Information provided by sailors at 2014 Worlds provided in person.

I trialed a Canting Mast and Hydrofoils on an A Class in late 2015, however due to not being an advanced Catamaran sailor, I cannot comment further on the Effects

Zombie Diffusion by peatar

I just saw that people seem to be interested in zombie apocalypses, so here we go:

The Zombie Apocalypse & what to do when it actually happens

Just like in my last post physicists/applied mathematicians came to the rescue of our purer colleagues by terming the previous, not so flashy-looking field of “diffusion models & interaction times” as zombie apocalypse! By now it should be obvious that mathematicians use every possible way of shameless advertising, so I’ll just stop pretending to be sorry about it.

So what is this all about? Why should we be interested in diffusion models and interaction times and what are they?

Assumptions: Assume zombies move like in the films, so pretty randomly with no real preference of direction (readers of my last post in this thread may identify this sort of movement as a Wiener process and indeed we will use the last post’s results!). Since we’ve got some randomness again one could try to get the expected/average number of zombies per square meter (or square mm, or even smaller, so this becomes a measure), but this is just the probability density function ρ of the last post, which happens to be the solution to the heat equation.
What do we want to calculate? Since this won’t really help us in the case of a zombie outbreak, let’s move on to something of interest like “How much time do I have to build a castle?“, or equivalently “What’s the expected time until a random particle reaches a certain destination?” which is also known as “mean first passage time”.
However, the “mean” time doesn’t help us much at all since the variance could be high; e.g. imagine they arrive either today or in one year (each with a probability of 50%), then the mean would be ~365/2 days, but this doesn’t really give us confidence.
So how about looking at the probability that they arrive at some time t? This can be defined as the L^2 norm of the difference of the probability density functions p_{x0}(. ,t) and p_{x1}(. ,t), where p_{x0}(x,t) gives the probability of a random particle starting at x0 to be at x after some time t (and analogously for x1).
How do we calculate it? This one’s a little bit tricky, but there are some pretty neat connections to the heat equation, Fokker-Planck operators and some other things I mentioned previously so if you’re interested feel free to take a look at my (first) Bachelor’s thesis (and references therein).
But this doesn’t have anything to do with reality! 1) We’re talking about zombies. 2) A valid objection might be that zombies do not move totally randomly. They could move randomly until they see brainzzz and then start to move towards brainz with a higher probability, but that’s pretty much the step from using the heat equation to using the Fokker-Planck equation! So the above considerations still hold for that case as well. Also it is possible to account for the geography (most of the works out there restrict themselves to the 1D case) by not doing all those calculations in some Euclidean space, but on some (compact, Riemannian) manifolds. Getting explicit solutions is pretty hard in this general case though, so numerical approximations (e.g. using some generalized Fourier expansion as shown in my thesis) are pretty much the best thing we can get.
Other things that might be of interest: Of course this is not the only interesting result since zombies exhibit a richer algebraic structure than random particles, or in other words: When they make contact with a person, this person will either die or become a zombie. From a mathematical point of view this is not any different than trying to model the spreading of diseases (or information in social networks) and since this is a serious problem quite a lot of work has already been done here which comes in handily for everybody interested in zombies.
Sources: So if you want to check out why we can’t continue to live in peace and harmony take a look at Mathematical Modelling of Zombies. In this paper they kind of “translate” the epidemiology vocab to zombie invasions and in this one they investigate the effects of urban street network topology on rates of infection spreading in zombie epidemics.

But what should I do if I encounter a zombie? In case you didn’t watch enough zombie films:


(or build a fortress and defeat every zombie that gets close to you)

Ito Calculus by peatar

Great idea for a thread, but I’m noting a serious lack of mathematics here so I’ll give it a go. Sorry for the sensational title, but it’s always hard to get people interested in mathematics.

(伊藤Ito calculus or Why Wall Street likes physicists

At first sight some sort of calculus for randomness, financial mathematics and physics may not have too much in common, so let me (very briefly) motivate theuse of randomness in financial mathematics (how it connects to physics will be dealt with later on) before it gets more technical:
Assume you want to model the price of some stock (let’s take some company that sells plants), i.e. you want to find a formula that takes everything you know about the market, your competitors, etc. and outputs what the prize of that stock will be tomorrow. Of course there is no way to do that with certainty (an unexpected drought may harm business, another competitor may get drunk and suddenly randomly start selling all of their stocks and in fact there are thousands of competitors so there are always some unforeseeable fluctuations, etc.), but not all is lost! We still can, at least to some degree, say something about how likely what outcome is, but I’ll leave the question on how exactly to model things to the financial mathematicians/economists.

What do we want to calculate? For now let us assume the size of interest is a function of something we cannot really control/predict (i.e. something we model as random). So we are interested in some F(B_t), where B_t is a Wiener process (think of it as a function that, for each time t, randomly moves in any possible direction with the same probability) and F is some smooth function (i.e. all derivatives exist and are bounded), then we are interested in the expectation EF(B_t) (=if we ran this random process an infinite number of times, what would its average be?).
How is it connected to physics? We find d/dt EF(B_t) = 1/2 E[d^2/dx^2 F(B_t)]. This basically follows from writing the Taylor expansion of F(B_{t+dt}) = F(B_t)+d/dx F(B_t)dB_t+1/2 d^2/dx^2 F(B_t)|dB_t|^2+O(|dB_t|^3), taking expectations on both sides and letting dt go to zero, while noting that EdB_t=0. Now this already looks almost like the heat equation and indeed, the probability density function ρ, implicitly defined by EF(B_t)=\int F(x)ρ(t,x)dx, is a solution to the heat equation d/dt ρ = 1/2 d^2/dx^2 (which can be seen by using the above result, the definition and integration by parts).
In particular the evolution of such a probability density function is given by the Fokker-Planck equation.
What does this have to do with Ito calculus? The “Ito-way” of putting this would be to write dF(B_t)=d/dx F(B_t)dB_t + 1/2 d^2/dx^2 F(B_t)dt. In fact the Ito calculus is something far more general and elaborate—maybe I will add a section on stochastic integration in the future.
How is this different from ordinary calculus? Usually this formula is compared to the usual chain rule dF(X_t)=d/dx F(X_t)dX_t which holds if the mapping t->X_t is smooth, but fails for Wiener processes since they are “only” (almost surely) continuous, but also (almost surely, almost everywhere) not differentiable, so the usual linearization argument X_{t+dt}≈X_t+dt*X’_t, used to derive the classical formulas, does not hold.

So how does this answer the question why Wall Street likes physicists?

  • The Ito calculus is used to derive the Black-Scholes equation (which entailed a Nobel (memorial) prize in economics in 1997) and people working with/on this model should know a quite a bit of the mathematical tools employed there (some of which happen to come from physics).
  • Obviously every physicist is (or at least should be) familiar with the heat equation and also have heard something about the Fokker-Planck equation. There’s also a fair share of them who still work on problems involving those formulas (the Fokker-Planck equation also appears in quantum mechanics) and hence are able to quickly grasp the underlying models used in financial mathematics. Apart from that, some of us mathematicians (who struggle to find fancy names like physicists do) simply call quantum mechanics “noncommutative probability theory” (there’s a reason for it!) and I think it’s somewhat reasonable to assume that probability theory has many applications in finance as well.

Warning: I don’t really know much about financial mathematics so if there are any economists around: Let me know about eventual mistakes.
Sources: Links in the text and Terry Tao’s blog.