Our new trampoline

Our old trampoline, which stemmed from when Miekie was tiny, about 18 months old, lasted very well until the second half of last year (i.e. about six years). Since then it's been on a path of accelerating decline, culminating in the spectacular abrupt simultaneous failure of multiple spring connections one day when I ran and leapt onto it. We had it repaired but that didn't last more than a few minutes!

An old photo I dug up of Pieter (who'd clearly just finished eating something) and Miekie (I shuddered when I noticed that she was running with a pair of scissors in her right hand!), taken ages ago, showing the old trampoline in the background

So yesterday we went and bought another, bigger, better and higher one, sized appropriately for a family of five, plus guests, plus a dog (if she feels up to it). It's even got its own safety net.

Just before the inaugural jump

Miekie and Pieter were joined in the inaugural jump by Tiaan from down the street

Soon Neil will be jumping too, I'm sure

Unfortunately Pieter got injured twice in rapid succession. First from an accidental blow to the chest from Tiaan's head and second by a blow to the face from his own knee. We got quite a fright after the second injury as Pieter was quite disoriented and sore, and had trouble talking and breathing. So we called paramedics who fortunately were here very quickly to examine him. Luckily he was given the all-clear and was just about back to normal within an hour or so! Now it's just Marisa and my nerves that still need calming.

Here's a short video of some happy jumping:

A different growth model

This is slightly technical, but oh well.

The exponential and linear growth models for Neil aren't going to be valid for long, so I've constructed a logarithmic model which should last far longer. The trick to constructing such models is that they should be relatively easy to parametrise. Most data tools like Excel or Google Sheets (which I'm using for Neil's data) have linear parametrisation functions so it's great if the model in question can be transformed into a linear form for this purpose. So I've constructed the logarithmic model with this in mind.

It is

where w is Neil's weight, delta t is the time since his lowest weight in days, b is a time scalar, e is Euler's constant, i.e. 2.718..., and epsilon is an error term, which I'd like to be as close to zero as possible. The parametrisation needs to set b and epsilon, as all other variables are already known. It would have been nice to have a third multiplicative parameter outside of the logarithm but that makes the model non-linearisable. So this will have to do.

Taking antilogs yields

which is nice because when you set

,

and

you get the familiar linear form

where x is delta t.

So, using Neil's growth data, it turns out that epsilon is -0.17 for now, which looks small, but is it? Considering the other terms in the logarithm, epsilon contributes just over 6% of the magnitude at delta t of zero and its relative contribution therefore just decreases thereafter. So, yes, the error is small* and the model fits well at this stage, with the largest apparent error at the time when Neil was at his lightest (i.e. two days after birth). Sure enough, this can be seen from the graph:

The thin green line is the logarithmic model

Now we need more data to see how long the model holds! This morning, while nobody else was listening, Neil and I discussed what we'd do once the model doesn't fit well any more. We thought of a nice way of segmenting his growth into more than one sub-model and elegantly joining the sub-models together using a very cool transition function, which I've been itching to use for some time now, but haven't had the chance. More on that in a later post though.

*Anything lower than 10% is pretty much 0 as far as I'm concerned!

Miekie's dress and Pieter's drawing

Miekie felt that she absolutely needed a new dress for Neil's christening so here she is wearing it:

(I should have forced the camera exposure settings to be constant when taking the photos... oh well...)

She's going to wear it to Marcus and Ali's wedding in April too.

Marisa bought Neil a nice shirt and a pair of trousers, and an very similar pair for Pieter.

On a separate matter, Pieter fell off a large plastic motorbike at a friend's house a few days ago. He drew the following drawing in his minimalist way to help explain to us what had happened:

I've annotated the picture to help explain what it's about:

Another growth update

It's been a very busy week with the result that while Neil was weighed again on Monday, I'm only now able to write a quick post about it.

Neil on Monday

His growth still fits an exponential model well, but the latest data point is slightly lower than the previous model suggested it would be. The overall time constant has also edged back up to 80 days because of this. A linear model also fits well and thus I've added it to the graph below.

It is, of course, inevitable that the rate of growth will slow soon so I'm going to devise a more complex s-shaped growth model once that starts happening. Luckily we should get another data point today as he's going for his six (and a bit) week check-up at his doctor.

The thin orange line is the linear growth trend

A walk

We went for another walk on the Irene Dairy Farm yesterday afternoon. Last time we went for a walk there was before Neil was born.

Waiting for our drinks

A never-ending stream of cows

Flight to Botswana

I flew to Botswana again this morning. As we flew over Midstream I took a few aerial photos, one of which is shown below.

Gaborone has had low water levels for quite some time. We flew over the Gaborone Dam, which is the city's main water reservoir, shortly before landing. There's water, but not much. Certainly not enough for very long, so hopefully there'll be some more rain soon.

Bulletjies

Pieter is very keen to participate in Bulletjie Rugby this year. Yesterday was an initial impromptu training session. The real kick off, so to speak, of the season will be tomorrow afternoon.

It looks as though Pieter and Neil will be great friends. Pieter is a very loving big brother and is able to sooth Neil to sleep by playing him CDs in his room and by pushing him around in the pram. Neil might turn out to be a bulletjie one day himself (assuming we'll still be living in the same province then).

Granddad's birthday

Miekie and Pieter made this using some stickers (click the image to see a larger version)

Having gone to bed later than usual last night, Miekie didn't wake up as early as she normally does. I made her coffee anyway, at the usual time, but it cooled off for longer than it does on most other mornings. Miekie didn't say anything about it but Marisa found this little hastily written note a little later:

Growth update

Neil was weighed again on Thursday. He now weighs around 4.8 kg. His growth curve (from discharge date onwards) is currently slightly super-exponential, as can be seen by the decreasing time constant (which I arrived at through refitting an exponential curve to the data with each new measurement). I've plotted the time constant in the second graph below. (The first time constant estimate is only based on two data points and could probably be disregarded, particularly in light of the large gap between it and the other two estimates.)

The pale blue line is the exponential trend-line which I've calculated from his discharge weight onwards (and mirrored back to his birth date, which highlights that the initial weight loss was far more rapid than subsequent weight gain)

The time constant looks as though it may settle at about 70 days

I'll abandon the exponential model once the time constant starts increasing significantly again (i.e. when Neil's growth factor starts slowing).

Miekie's birthday party

Miekie's birthday party was finally held at our house yesterday afternoon. Marisa took most of these photos as I had to be in Botswana. Luckily Marisa's parents were there to help with everything because it's quite a feat hosting a multitude of young girls.

During construction of a piñata, the day before the party