Simon blogs

[Simon]

The weather has become cooler again, that is very nice. It's still deep in the shorts-and-T-shirt weather. I wear sandals whenever possible, that's good for the environment because I don't have to launder any socks.

There will be a Family Feud round (forum game) by Forestidia and me, we'll think of the questions within a week.



Comma, more base-16

Germans use decimal commas and thousands-separating points: 1.234,5. That is weird and should be abolished in favor of the decimal point, 1,234.5, which seems to be more common around the world than any other separator. It's extremely confusing to read any kind of number in German when you're exposed to the decimal comma 80 % of the time.

Decimal is bad anyway and should be swapped for hexadecimal (not for base-12 even though many anti-decimal people want base-12). Powers of 2 are so useful that any other prime merely bloats the base, and 16 has an integer root (4) to generate patterns in the base-16 multiplication table that help memorizing the table.

■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■

The human brain is good at pattern recognition. It's also excellent at halving a visually presented quantity. Base-16 exploits that. A square tiled into 4x4 small squares is easier to grasp than a rectangle tiled 5x2 because of the 4x4's regularity and smaller max side length. Thus, let's design our numbers for humans, not for traditionalists.

Base-16 coins should be square (maybe some should be triangular?). They won't roll under the sofa, and they should get little tongues and grooves along their sides, then you can stick together 4 one-euro pieces to from a single 4-euro piece. The smallest coin available should be a 16th of a euro, anything smaller is unnecessary. In 30 years, even the 1/16-euro coin will be phased out, and the 1/4-euro will be the smallest.

No coin should be twice the value of another; coins should be a factor of 4 apart (maybe even 16 if coins can form a 4-times-larger coin by sticking them together). There should be as few different coins as possible and they should be easy to tell apart both by feeling and by looking.

There is no compelling reason to use base-10 other than tradition. The 10 fingers on our two hands seem like an after-the-fact rationalization of the bad choice that is base-10. Really, we don't have 5 similarly-shaped fingers on a hand; rather, we have 4 fingers and an opposing thumb. With 4 = 2^2 fingers and 1 = 2^0 thumb, we have 2 = 2^1 kinds of different stuff on each of our 2 = 2^1 hands. See, even nature ditches anything but powers of 2!

-- Simon

[Dullstar]

While the main reason to use base-10 is tradition as you've said, I think that in this particular case, the tradition argument carries a lot more weight than it normally would.

If you were designing everything from scratch, it *may* make sense to use base-16 from the start, rather than base-10. But we can't ignore the fact that base-10 is deeply ingrained, because this imposes a series of problems we would have to deal with in order to switch. In this sense, I think it would be a very, very, very long time (probably at a minimum several generations' worth of time) before any possible advantages of base-16 would make up for the costs (financial or otherwise) of the transition process.

Disadvantages of switching from base-10 to base-16:
- Most people have to learn a new number system (most people probably don't even know what base-16 is, let alone how to use it)
- Confusion regarding values represented by numbers in works prior to transition
- Ambiguity regarding values represented by numbers in works during transition (if you have the number 52, did the author mean that in base-10 or base-16? Most likely, not everyone will switch right away)
- SI system prefixes become harder to work with unless they are changed, in which case the world has to redo the transition to SI.
- Thought the fact that the US culturally refuses to use SI is confusing enough? Wait until any country decides they just don't feel like transitioning to base-16. Now, in order to understand any numerical values containing only the digits 0-9, we must know if it was produced in a country that used base-10 or base-16 at the time of production. At least with units, they have to be labelled, so there's no ambiguity regarding whether a paper intends a length to be interpreted in feet or meters.
- To eliminate any confusion, we'd have to start clarifying bases by some way, either by inventing new symbols for 0-9 in the base-16 system, or by giving a base label of some sort to every number. This will be much less convenient than the current system where we are almost always safe to assume a value is in base-10 if no base is specified.
- New number words would need to be created, at least in English, for numbers such as 2A (how would you even pronounce that? twenty-A?). New ones would also be needed in order to eliminate the ambiguity discussed earlier.

I'd say that in a realistic best case scenario, this change would create a situation where instead of just worrying about whether 1,234 is between 1000 and 2000 or 1 and 2, now we have to worry about whether 1,234 is 1,234 or 4,660.

[nin10doadict]

As a follow up to the 'pronouncing hexidecimal numbers' thing... Consider the number AD. How to say that? "Ay-dee" sounds much like eighty. "Ay-dee-dee?" How do we know that doesn't mean 8D? Would it be better to just read off every number one digit at a time? Perhaps add pauses in fixed locations for long numbers.

Anyone who's studied computer science should have an understanding of hexidecimal, but having it replace base 10 entirely would be a lengthy process that would encounter much resistance.

[Simon]

Dullstar and nin10doadict, thanks for the wise responses! Yeah, the tradition argument weighs heavily for base-10. I don't expect a serious real-world move away from base-10 in my lifetime.

In the dark corners of my mind, I want to see the world struggle, in all gruesome details, for the better future. The switch to base-16 would be our generation's gift for the children in 20 to 50 years.

Designing new words for numbers: Yes. We must distribute 16 unique digit names in the space of all short, nice words/sounds such that no two of them are too close to each other.

Even today, eighteen and eighty sound far too similar. I want to call 18 ten-eight.

-- Simon

[mobius]

we could use a smaller number of symbols then alter them (like rotating 90 degrees for example) to represent higher or other numbers.

I always loved the fictional 'D'ni' number system from the Myst series;

it's a base 25 system, except there are actually only 4 symbols. Number 5 is 1 rotated, then 6 is 5 combined with (or superimposed with) 1. 7 is 5 with 2 etc. Then 25 and onward work similar to our 10, 11, etc.
Though I don't know if I'd describe this as 'better' compared to our system

http://dni.wikia.com/wiki/D%27ni_Numerals

[ccexplore]

I always loved the fictional 'D'ni' number system from the Myst series;

Ah yes, I remember playing that game back in my teen days, fun times.  I was able to work out the number system on my own, but kind of wonder how many people might have gotten stumped by it?

While base 25 is a reasonable description for the system, considering that the in-game mythology actually holds the number 5 as special, it is equivalent but perhaps somewhat more fitting to say it's a base-5 system with a unusual writing system for the "digits", where effectively you group them into pairs and rotate one of the two but otherwise write them out both overlapping in the same space.  Basically imagine if instead of writing "13" for thirteen, you are to rotate the 1 ninety degrees so it becomes more like -, then you write both digits overlapping each other so you end up with something like a 3 with a - going through it.  It's equivalent to think of such a system as both "base 100" as well as "base 10 with an unusual system of writing out the digits".

[Simon]

PhD

I defended my doctorate thesis today. It's a magna cum laude, 2nd best of 4 possible passing degrees. It's an excellent result, I didn't expect it this good at all. The thesis itself didn't get such a good grade, but the presentation and public quiz convinced the committee.

Forestidia said: The Jazz speedruns and the streaming helped me for sure with presenting, I talked loud and clear. Icho was there, too, and congratulated. This was even a spontaneous 3-person forum user meeting.

Technically, I'm not allowed yet to call myself doctor or PhD; that has to wait until October.

The next days, it's all chilling and getting up to speed with friends. Then, job hunting!

-- Simon

[Ryemanni]

That's worth a good ol' warm Congratulations!

[Akseli]

#neolemmix IRC channel logs Monday the 30th of July 2018:

[02:27:17]    <SimonN> Han nan nan nan, Akseli, I still have to defend to get the degree, and the degree is in maths, not in busting quacks
[02:27:31]    <SimonN> busting quacks, one learns that on the internet better than at any uni
[02:29:18]    <Akseli> are you saying your field is more hardcore than other fields? : P
[02:30:04]    <Akseli> just kidding, good luck for the defending : D I've been in three different defending events, they're fun at least here in Finland
[02:30:07]    <SimonN> no, merely that my field is unrelated, anybody can compute acceleration : )
[02:30:23]    <SimonN> heh yeah, it should go well
[02:30:39]    <Akseli> people are just laughing and telling jokes
[02:30:47]    <Akseli> the audience goes wild
[02:30:56]    <Akseli> everyone has a festive feeling
[02:31:00]    <SimonN> hoh, nah, we take it slightly more seriously
[02:31:06]    <Akseli> : D : D : D : D
[02:31:13]    <SimonN> it's mostly about the math still
[02:31:31]    <SimonN> the audience that is not well-versed in the field has a hard time following
[02:32:36]    <Nessy> : D
[02:34:45]    <Nessy> Yeah good luck Simon!
[02:36:23]    <SimonN> thanks!
[02:41:24]    <Akseli> yeah Simon, overwhelm the counter argument guy !
[02:42:23]    <SimonN> "why did you spend years on this trivial stuff?" -- "if it's trivial, why has nobody else done it yet?"
[02:42:42]    <Nessy> > ; P
[02:45:59]    <Akseli> yes, and the audience enjoys their life
[02:46:15]    <Akseli> "ha ha ha" echoes in the room
[02:46:23]    <Akseli> the counter argument guy blushes
[02:46:34]    <Akseli> Simon flashes his overly charismatic smile
[02:46:41]    <Akseli> people go wild yet again
[02:47:28]    <Akseli> after 2 hours and 7 minutes the event is over, and people gather outside the room to chat in joyful manner

____________________

Congratulations, Simon!

[IchoTolot]

Congratulations here as well.

I even understood some single things during the defense and the buffet afterwards was splendid!

[Nessy]

Another BIG congratulations Simon!

You worked very hard on this and you should be proud of your accomplishments!

[nin10doadict]

Sounds like you'll be getting more out of your degree than I've been getting out of mine. Best wishes

[ccexplore]

Congratulations!  Looking forward soon to reading "Dr. Simon blogs".

[grams88]

That must of been tough going, well done Simon. All the studying has been worth it.

[Simon]

Thanks everybody for the kind words!

-- Simon