Self Isolation In Bonavista

[ChrisGreaves]

It is now 417.112 days since I began self-isolation in Bonavista (that would be 417.174 days Newfoundland Time) and am considering coming out and exposing my obsession with Roman Numeral notation implemented on Turing Machine technology as envisaged by Alan M. Turing.
You can look up Alan M. Turing on this new-fangled internet, providing that the café isn’t shut down, or you could read about him in a book if the public library wasn’t shut down.
What price the Information Age?
Anyway, I have attached a PDF file for comment. Don’t try reading it if you are under 65 years of age, because it talks about things that you won’t have seen on a clock dial in your lifetime.
(signed) “Timid” of Bonavista

[stuck]

... this new-fangled internet, providing that the café isn’t shut down... ...the public library wasn’t shut down...

So how are you managing to access the outside world?

Ken

[LisaGreen]

I remember my first intro to Turing machines...

The emperors new mind... Roger Penrose.

Lisa

[stuck]

...Roger Penrose...

Get him to do your bathroom, he's well know for his tiling.

Ken

[ChrisGreaves]

So how are you managing to access the outside world?Ken

With difficulty. My good friend Tom invited me over.

I miss Eileen's Lounge, although it ought not to miss me.

I made my monthly off-shore banking transfer and paid our mutual friend $275 that I owe her. but am getting much work done on my computing projects, house organisation, and have cleared almost half my driveway of snow.
It is, as I tripe, snowing again ....

My 250 bulbs planted last October have not yet bloomed.

Cheers
Chris

[ChrisGreaves]

...Roger Penrose...

Get him to do your bathroom, he's well know for his tiling. Ken

Ooooh!
Bags I first shot at an interpreter for Tiling Machines!
Cheers
Chris

[John Gray]

Chris: do you have any evidence of yer Romans using fractional (or decimal) notation in their number system? Did they have any notion of the concept of a decimal point? If not your paper seems to be a theoretical exercise!

"And another thing" [!], you do not treat the occasional appearance of (say) VIIII instead of IX on ancient clock faces.

Also see Wolfram Research's page on Roman Numerals for some history about the notation.

[jonwallace]

"And another thing" [!], you do not treat the occasional appearance of (say) VIIII instead of IX on ancient clock faces.

I have two clocks with roman numerals on their faces, the oldest was my granny's and was made before WWII and the newest was presented to me on occasion of 25 years with the NHS. Both have IIII and VIII instead of IV and IX. My understanding is that clock makers preferred the aesthetics and thought they looked nicer that way...

[Nick Vittum]

Chris: do you have any evidence ... If not your paper seems to be a theoretical exercise! ....

I had assumed that tongue had been planted firmly in cheek while writing...

[GeoffW]

Both have IIII and VIII instead of IV and IX.

A clock which has 8 instead of 9?

It's common to use IIII on clocks, but it's not universal - Big Be uses iv (lower case). It seems VIIII is often used, but not as common as IIII.

The reason? There are many theories but none conclusive

[jonwallace]

Both have IIII and VIII instead of IV and IX.

A clock which has 8 instead of 9?

*Sigh* I knew I should have been paying attention to what I was typing and not to her telling me how to cook macaroni cheese in a slow cooker...

[ChrisGreaves]

John, My apologies for the late response. I have worked this far down my ToDo list now that I am online. No need to resurrect thr thread, I wanted to acknowledge your response and not ignore you!


Hello John, and thank you for your comments/questions.

Do you have any evidence of yer Romans using fractional (or decimal) notation in their number system? Did they have any notion of the concept of a decimal point?

None whatsoever, that I know of, but that won’t stop me. I am trying to think not of a decimal point but a Roman Point. “decimal Point” keeps swerving me into thinking “rational part of ten” From the few books I possess on Number Theory, I see no mention of Roman Notation.
Yet the Romans must have torn a loaf in half and argued over who had the bigger portion, else what are Stupid Big Sisters for?
There must have been a mental concept of (say) “a half” or “a third”.
If I’ve got my terminology right, I am thinking not of Real Numbers, but of Rational Numbers, formed as a ratio (hence rational) of whole numbers, which are numbers without a fractional part which is the rational part … but this way madness lies.
So I was thinking more of a ratio as the fractional part.
To that end a half would be one of two equal parts of “one”, hence the “two” (or “II”) in my use of “<period>II”.
And hence “one 74th of my life” would be represented as “<period>LXXIV”.
I didn’t really want to use fractions as part of a quantity as I wanted to employ them as exponents, and hence to explore roots of numbers. The expression “XVI^<period>II” should turn out to be equal to “IV”.
But most of this is irrelevant.
In the Turing Machines I cheat at arithmetic in Roman, by converting Roman through Decimal to Binary; doing the +-*/^ in Binary, and then converting the Binary result back through Decimal to Roman. I am not as clever as you don’t think I am.

If not your paper seems to be a theoretical exercise!

Indian.png

Theoretical is fair enough, but then so too was my little foray into converting to a “base negative four” number system. I was raised in Decimal, lured into Binary, and some ten years ago recoiled in horror at a Canadian firm that was shy of an Indian client who used Lakhs of Rupees. I found it no different from Pounds, Shillings and Pence (and to keep BobH happy, Guineas and Florins). That set me wandering off around number-base systems.
In fact, while typing that I started thinking about a Turing machine to convert Binary to any integral base; or – why not? – any fractional base.

"And another thing" [!], you do not treat the occasional appearance of (say) VIIII instead of IX on ancient clock faces.

IX, mein freund, I’d VIII to IVGo a Xdency II be a III-thinker In this matter!

Cheers
John

[GeoffW]

Re fractions in Roman numerals :
http://mathforum.org/dr.math/faq/faq.roman.html#calc