Category Archives: maths

VerifAI

What’s wrong with me? I no longer have the urge to check when someone on the internet mentions an AI getting things wrong; you know, hallucinating (offering demonstrably false statements as facts).

An increasing number of reports of such behaviour appear to be completely fabricated either for the lolz or as another reason to not use AI, but some are verifiable.

It’s undeniable that AIs or large language models (LLMs) are an increasing part of modern life, and whether one personally participates in the hype/bubble/de-skilling of not. But I’ve concluded that it’s pointless to fact-check posts. Why?

Other than using an AI how else is there to find out whether someone is making something up?

Humans don’t want to hear things that upset their worldview. We saw it writ large at the height of the COVID-19 pandemic, we’re seeing it with the rise of populist, far-right politicians. We should be checking stuff the little people in our phones or on our computer and TV screens are saying, and yet we don’t.

Why? Despite the decades-old dream of artificial intelligence giving us time to do things that enrich our lives, it’s not really come to pass has it. But it really can’t be far away now, right?

All the media chatter is of knowledge transfer, of chatbots supplanting interactions between humans, of ‘coming here and stealing our jobs…’ of the billions spent by the billionaires on the data centres required to keep AI running… and of the billions written off by the billionaires as each technology hits an evolutionary dead end.

It looks to me like Facebook’s ‘move fast and break things’ motto won out over Google’s ‘do no evil’. And it’s boundless.

A heart-shaped 'tuft' of grass, buttercups and probably dandelion leaves left over after mowing our back lawn towards the end of 'No Mow May' – mowed early due to the forecast of lots of rain. Photo taken during the early evening and facing roughly north; the shadows are long enough to split the heart in two but the sun is high enough to not have the fence shadow obscure the top of the tuft. A vaguely human's shoe-clad feet appear at the bottom of the photo. Photo by the vaguely human foot custodian.
A heart-shaped ‘tuft’ of grass, buttercups and probably dandelion leaves left over after mowing our back lawn towards the end of ‘No Mow May’ – mowed early due to the forecast of lots of rain. Photo taken during the early evening and facing roughly north; the shadows are long enough to split the heart in two but the sun is high enough to not have the fence shadow obscure the top of the tuft. A vaguely human’s shoe-clad feet appear at the bottom of the photo. Photo by the vaguely human foot custodian.

There’s not much yet of the increasing cost of AI to business as the subsidies start to become economically unviable for the AI peddlers, and there’s not much yet of the cost to humanity.

The cost of the AI ‘arms races’, like the cost of climate change and the cost of COVID denial, is an inconvenient truth that ordinary humans don’t want to confront.

And then there’s this, an excerpt from Carl Sagan’s ‘Pale Blue Dot: A Vision of the Human Future in Space’ (Goodreads link and a link to one of The Planetary Society’s videos of Dr Sagan):

“From this distant vantage point [that of ‘an alien scientist newly arrived at the outskirts of our solar system’ where Voyager 1 took the photograph], the Earth might not seem of any particular interest.

“Look again at that dot. That’s here. That’s home. That’s us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every “superstar,” every “supreme leader,” every saint and sinner in the history of our species lived there-on a mote of dust suspended in a sunbeam.”

This should make us all think. And yet…

Pocket Calculator

I just acquired a Casio fx-102 (Reddit r/calculators link) calculator – a device rooted firmly in the days when the display illuminated without a backlight such that it could be read at night. So you can’t see the buttons, so what?!

Buttons.

A Casio fx-102 calculator resting on its slip case. The display reads 5318008 - something familiar to anyone who's ever turned a calculator upside-down.
A Casio fx-102 calculator resting on its slip case. The display reads 5318008 – something familiar to anyone who’s ever turned a calculator upside-down.

And it’s not exactly pocketable, it’s wi-iiide. And sadly it does not play a little melody when pressing down a special key. So much for me trying to fashion an easy link to the Kraftwerk song (from 1981).

Ok, it has a 12-digit green LED display and it’s quite frankly awesome. The input method is straightforward for most people (it’s not RPN). It’s old-school operand-operator-operand… and there’s no computer algebra system, no brackets, no built-in constants apart from pi (and e), no persistent history or memories…

Speaking of memories…

My dad bought our family’s first pocket calculator in the 1970s – also a Casio, also with a green LED. I bought Casio calculators until the late 1980s, at which time TI and HP…

…so anyway, this, the new-to-me fx-102, is from 1976.

It’s 50 this year.

Fifty!

Happy Birthday to you… 🎵

Browns vs Fibonacci followup

There’s a fundamental flaw in my reasoning in my recent post – it stemmed from a willingness to believe the starting point I chose had a more direct relationship to the team’s overall performance during the past few years.

I made amendments after some useful feedback in Reddit’s r/Browns, picking a different entry point – the year I became a fan. It brought a more simplistic summary of the Browns:

We lose for 2 seasons and get into the playoffs every 3 seasons.

Loss-loss-playoffs-loss-loss-playoffs, etc.

2018-2019-2020-2021-2022-2023-2024-(2025)-(2026).

Sure the sample size is limited, but I want to believe we’ve another playoff appearance in 2026.

Super Bowl?

Shuggie Bear and a Frawg wearing a Cleveland Browns helmet. They're stood and sat in a totally realistic lily pond.
Shuggie Bear and a Frawg wearing a Cleveland Browns helmet. They’re stood and sat in a totally realistic lily pond.

Browns vs Fibonacci

Fibonacci (also known as Leonardo Fibonacci, Leonardo Bonacci or Leonardo Pisano) was born in Pisa, Italy in 1170 and died around 1250. He was a talented mathematician1 probably most famous for popularising the Arabic numbering system and a number sequence named after him – The Fibonacci sequence or Fibonacci numbers.2

I, on the other hand, am not a talented mathematician. I’m a Browns fan.

Nevertheless I’m about to link Fibonacci numbers – more precisely the Fibonacci spiral3 – with the performance of the Cleveland Browns onwards from the disastrous 2016 and 2017 seasons.4 Note, not attempting to link, actually linking.

By the way, before the mathematicians shout at me, though closely linked to the Golden spiral5, Fibonacci’s is composed of a series of 90° arcs within squares of increasing size. It’s not a ‘pure’, continuous geometric shape thingy.

Here’s an image rotated from the Wikipedia original of the Fibonacci spiral in coloured squares, numbered upto 216.

A Fibonacci spiral, with the 1 ,1 ,2 ,3, 5, 8, 13 and 21 squares coloured respectively white, magenta, purple, blue, cyan, green, orange and red. The image and thus the numbers are upside down because it better-illustrates the point I wish to make.
A Fibonacci spiral, with the 1 ,1 ,2 ,3, 5, 8, 13 and 21 squares coloured respectively white, magenta, purple, blue, cyan, green, orange and red. The image and thus the numbers are upside down because it better-illustrates the point I wish to make.

We shall start on this silly journey with the Browns 2016 season represented by the white square. 2016 was bad for the team. Really bad. 1 win from 16 games played. The arc goes up a bit and to the left.

2017 was bad. Worse. Absolutely dire. So the arc in the magenta square drops to the left, representing the zero (0) wins from 16 games.

Now 2018 is when I became a fan of the team. Although the purple arc goes downwards it goes to the right. 2018 brought 7 wins and a tie (!) from 16 games. Woohoo! It was a season of promise, of hope. And we got rid of Head Coach Hue Jackson. Which was nice.

In 2019 the progress regressed a bit, to 6 wins from 16 games, so although the blue arc goes up and to the right it doesn’t fit this scheme I’m outlining. 2019 was generally seen by Browns fans to be a disappointing aberration, so I’m giving Fibonacci a pass on this one. He’s no Nostradamus7 so couldn’t have foreseen Head Coach Freddie Kitchens – promoted beyond his ability at the time.

2020, wow. Cyan, numbered ‘5’. The curve goes up and to the left. An 11 win season from 16. We vaulted into the playoffs, beating the steelers twice in succession, and only falling to the Kansas City Chiefs in the Divisonal Playoffs. Probably the most enjoyable season of football I’ve ever seen. Kevin Stefanski, Head Coach of the Year.

Now, in 2021 you’d expect the team to capitalise on the preceding season. But no. The green arc goes downwards and to the left. We won 8 games from the expanded schedule of 17 games. Not great. Injuries at crucial positions screwed us over and so disappointment was again the order of that year.

And then we lost quarterback Baker Mayfield.

2022? Orange, down, right. Regression again, 7 wins from 17 games. Injuries. Meh.

In 2023 we won 11 games from 17. We got into the playoffs and fell immediately to the Houston Texans. Red square, upwards and to the right. We did it with a quarterback dragged off his sofa halfway through the year and plugged into the offense. Joe ‘Elite Dragon’ Flacco.

Still with me?

Let’s carry the sequence on then, for the 2024 season just ended. For us at least. A mere 3 wins from 17 games. So, what does the arc do with a teeny bit of extrapolation? Up, to the left. Colour? Black I’d imagine. Even accounting for our quarter-billion quarterback woes this was a bad one.

Season W-L-T Fibonacci
2016 1-15-0 ↖️
2017 0-16-0 ↙️
2018 7-8-1 ↘️
2019 6-10-0 ↗️
2020 11-5-0 ↖️
2021 8-9-0 ↙️
2022 7-10-0 ↘️
2023 11-6-0 ↗️
2024 3-14-0 ↖️
2025 Who knows? ↙️
Browns vs Fibonacci

2025 will have an arc heading down and to the left. Pain for us fans? Of course it is, we’re Browns fans. Colour Brown then? It’s expected that 2025 will be a rebuilding year of sorts for us. Fans are already talking about the dearth of quarterback talent in this year’s draft and so pushing for a mediocre-to-tanking season to get a better 2026 pick.

I’m not one of those fans.

But you can’t argue with the mathematics of all this.

Can you?

Of course you can.


When I posted a version of this to the r/Browns subreddit someone made the point that since Coach Stefanski arrived it’s been a win-lose-win-lose sequence. That’s not entirely true, it’s actually been win-lose-lose-win-lose-lose, etc.

And so I updated the chart:

Season W-L-T Fibonacci #, coach
2018 7-8-1 1 (HJ,GW)
2019 6-10-0 1 (FK)
2020 11-5-0 2 (KS)
2021 8-9-0 3 (KS)
2022 7-10-0 5 (KS)
2023 11-6-0 8 (KS)
2024 3-14-0 13 (KS)
2025 Who knows? 21 (KS?)
2026 Super Bowl! 34 (KS?)

There’s a pattern. 2018 and 2019 (before Stefanski arrived) improved on the preceding 2 seasons, but weren’t great. The Fibonacci numbers are odd.

2020 showed up as an even Fibonacci number, and we reached the playoffs. Remember this.

2021 and 2022 again brought a slide in results – odd Fibonaccis both.

2023 was an even numbered year, and we reached the playoffs. Which was nice.

2024, predictably as far as I’m concerned, brought a desperately deep low in my fandom. An odd-numbered year.

2025, well, as an odd Fibonacci I expect nothing better than misery.

But, as the table clearly states, 2026 is going to be a Super Bowl season; we Browns fans should expect nothing less!


Footnotes? Oh yes!

  1. The life, works and legacy of Fibonacci (Wikipedia).
  2. The Fibonacci sequence (Wikipedia).
  3. The Fibonacci spiral (Wikipedia).
  4. A List of Cleveland Browns seasons (Wikipedia).
  5. The Golden spiral (Wikipedia). Linked here for the continuously zooming/magnifying image at the top of the page. Oooh, mathematics porn!
  6. Wikipedia image by Romain, credits.
  7. Noted seer Nostradamus (Wikipedia).