Another week

Another week has passed by so quickly! There's nothing much to say as it was rather uneventful. Here are a few weekend photos.

On our Saturday afternoon walk

The two brothers spending some time together before lunch on Sunday

The first meal where the five of us were all together was Sunday lunch (normally we time meals around Neil's sleeping times)

Goldilocks Alexander and Misha popped in for coffee on Sunday afternoon

We're all looking forward to the next few weeks very much. Gomutti arrives on Wednesday and Granddad on Sunday. Then we're all off to the Cape next Wednesday for almost two weeks for Marcus and Ali's wedding.

A weekend away

It has been our first weekend away with Neil. We went to Sondela which, as Marisa pointed out, happens to have been our previous weekend-away destination too, which was before Neil was born.

We booked three chalets next to each other. One for us, another for the Kotzes, i.e. Nel, Magdeleen, Amelie and Ingrid, and the remaining one for the Bothas, i.e. Marius, Evelyn, Trevor and Patrick.

Sondela's Nyalas are as nosey as ever

 

We spent a lot of time at the swimming pool

Pools and ice cream tend to go together

No swimming nor ice cream for this little one yet

We spent less time driving around looking for animals than we normally do. But we did manage to fit in one drive...

On the way home we popped in for tea at Kobie and Anelle. It's Anelle's birthday on Monday.

Christening details

Neil's christening is to be held on Sunday 29 March at 18:00 at the Midstream Familiekerk. This is the invitation to all family and friends who'd like to be there:

(Click on the image to see a larger version)

New helmets and a few other photos taken over the weekend

Miekie and Pieter have new cycling helmets which they wore for the first time on Saturday:

Marisa took this photo during the assembly stage of the new trampoline on Saturday:

The worker (me) plus two quality control agents

Neil has to endure a quick kiss on the tummy from me now and then

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