In Series …
Local (personal, potentially shallow, and subject to change) outlooks on science, technology, growth, and occasionally culture and history. I aim to write an essay every week, but whether it can make its way to FWPhys is random. Hence the series title.

Part of me thought it might be fitting to dump the following thought threads out of my brain, where a coarsely implemented make-believe persona of a health counsel suggested it might be for my own benefit.

eyes on logarithm

In my context, semilogy doesn’t have anything to do with that cool humanities subject related to semiotics or Dan Brown. The word arose during my early days learning Python and MATLAB as a private joke. There, “semilogy”, was a command used to plot a Log-Linear graph, and I somehow made it a personal joke to always pronounce it /’sɛmilɒˌʤɪ/, until that confused some of my own Python workshop students.

My recent main-line of research work deals with numerical artefacts and floating point errors a lot, so plt.semiology has become something that I use quite often. And somehow some of my subconscious thoughts evoked by seeing log plots day in and day out diffused outside my professional work, and hence this short note.

When I began reading those damned (❤️) popsci magazines when I was about 5, I came across e quite naturally early on — in perhaps an illustrated short story that I no longer recall the details — and my econofinances-backgrounded parents told me the number is known as ‘Limit’. Not Euler’s or Bernoulli’s constant or the more common name “base of the natural logarithm”, a limit.

Limit for what? That took me more time for me to truely grasp than I care to admit. But as you may know today,

lim(n->∞) (1+1/n)^n = e.

In other words, (e-1) is the limit on the annual return in a compound interest scheme that has an annual interest rate of 100%, as you compound more and more frequently within that year.

Of course, the discussion of e‘s mathematics and their applications easily fill library shelves. The endless river roars past; I scoop with a mug, and only drink what I can. Be it the methodology of this blog, or part of my new life philosophy.

Anyways, has this been what haunts my mind?

Catching up with a linear brain

I recall my brief stay back home in January 2020, and the surreal feeling seeing the COVID global numbers grow from 10 to 700 in mere days. The initial outbreak evoked a fear that humanity might yet again expose itself to the subversion of an exponential enemy. I am fortunate that the virus only got within 50km or 2 degrees of social connections to me early 2021, but remain undecided on how optimistic I should view the future for the global civilization.

Back to the main note.

There are, of course, subjective experiences that cope with exponential nicely and naturally. Hearing (dBa) is one example. But most don’t. There’s a famous little quiz given to zing people: say you have a bacterium culture that doubles in size every day, and the culture takes over the Petri dish on day 10, when was the dish only half-covered? Day 9, you realize, surprisedly or otherwise. On day 5 — the temporal midpoint — it probably wasn’t even noticeable to the eye, taking only 3% of the space.

In my brief interactions with aspiring or accompli change-makers in various networking occasions in Auckland and San Fran, this conflict is particularly palpable. How many a device / service / business model / concept began so painfully slowly, but took over the little shared awareness of people so quickly in the end.

Another kind of exponentiation that starts conversations and maybe more is the basis of class stratification: economically, earning linearly — using time and sweat to beget one’s main income — and earning exponentially — using money to earn money — supports lives on this planet so different they might as well be apart. 1% of interest can work wonders over centuries, even though the people pass and went that saw it happen probably did not or could not register.

I somehow wanted to link the same feeling of “two worlds” to my nervousness before my first publication, hoping that there will be a time in the future that I am exponentially more effective and productive. But that I’d rather keep private.

For the first time, upon observing and internalising these phenomenon, I think I understood our time’s myriad mindsets and means to financial liberty — the particular bandwagon isn’t important; diversity is the brand of our time — around the world, since the beginning of modern society, people have been attempting to abandon one path, journeying through parts unknown, and hopefully joining the other,

I don’t know why I, a partial, unwary, and overly confident participant of society (more like the physics dining room), am here babbling about the stuff above. An internal transition to begin considering a career in industry perhaps — I don’t know if it is a welcome one.

On the other hand, A purer quantum or astroparticle theorist may take the time to remind you that every e^x looked like (1+x) for a while. So who’s to say a certain path is linear forever?

Ending notes: The Exponentiation of Oversimplification

Of course, not all small distortions grow up to cover the entire petri-dish, and even the Logistic model (that takes account of the eventual depletion of resources due to overpopulation) is oversimplified. I tried to forcefully attach my typical early 20s confusion to mathematical facts, and I know it will not come across as coherent to others.

Do I have a final lesson for today’s piece? A word worthy of remembrance?

Linear or exponential, or the countless ways through which our world changes, or the countless more ways that change happen we can’t quantify, there is an uncertain future up ahead, and instinct alone might not be sufficient equipment for us to deal with them.

— Unless if you argue that reason, the courage to seek things outside our wishes and prejudices, are part of this instinct.