He tries counting sheep to fall asleep, as per cliche, but his mind won’t shut off and he starts free-associating. Square root of nine for three, then IV for four…which leads to a centurion sheep leading a full unit.
That looks like more than just one unit, if the “148” is an accurate count of the “flock”.
My favorite rock concert album and video were “Velvet Underground Live MCMXCIII”. Which devotees know to say aloud as “em cee em ex cee aye-aye-aye”.
You know what year that was done, too.
In the first panel, it’s clear he’s counting sheep to get to sleep.
In the second panel, you see the square root of 9 (which is 3). Here’s where the reader sees that more creative ways of counting are being introduced.
The third panel has two parts: The first part shows “IV” (the Roman numeral for 4). Along with the sheep in Roman regalia, this goes along with the trope introduced in the second panel, in that more creative ways of counting are being used.
But then there’s the third panel’s second part: “CXLVIII” and it being represented with a legion of sheep in Roman soldier garb. That’s kind of confusing, so what’s that all about?
I think it’s just a visual pun that showcases the difficulty of Roman numerals. Let’s face it, once you get to “IV” (I plus V is… 4?) things get a little wonky in the Roman world of numbers. (What’s after “IV”? IV + I, right? So, “IVI”?) And if “IV” isn’t confusing enough for you, I’m sure that “CXLVIII” certainly is.
Personally, I think that the strip would be slightly clearer if the “IV” sheep was placed in its own separate panel (the third panel), and the “CXLVIII” sheep were placed in the final fourth panel. That way, the creativeness of counting sheep is established in the first three panels, and the confusion of Roman numerals is kept separate in the fourth panel.
In case any reader here is relatively unfamiliar with the Dark Side of the Horse comic, the “counting sheep to fall asleep” trope is one of those he reuses frequently and takes joy in twisting into unexpected variants. Maybe second only to “elevator triangular call buttons” and slightly ahead of “highway roadside hazard warning signs”.
Most kids learn Roman numerals in school, but my knowledge of them was perfected by watching “Looney Tunes” every Saturday morning. Even as kids, we observed that the copyright date in the opening credits was a fairly reliable indicator for the quality of the upcoming cartoon. The best ones were dated 1951-53 (MCMLI to LIII), anything before that was usually too corny, and anything 1956 or later was usually garbage (with some notable exceptions).
P.S. Chuck Jones was the most reliable director, but an even more reliable indicator were stories written by Michael Maltese.
P.S. @ J-L – There are some exceptions, but DSotH is almost always a three-panel strip.
” Let’s face it, once you get to “IV” (I plus V is… 4?) things get a little wonky in the Roman world of numbers. (What’s after “IV”? IV + I, right? So, “IVI”?) And if “IV” isn’t confusing enough for you, I’m sure that “CXLVIII” certainly is.”
Um…. no…. I always considered Roman Numerals to be very straight forward, a number to the left of a larger means to subtract from so IV must be read as V- I which is ….. 4? well, yeah….. and IVI = V-I+I=V. Although there are semantic rules of cleaning and not going exceeding magnitudes in subtraction… such thinking is useful if you try to add/subtract/multiply roman numerals without decimal conversion[*].
And CXLVIII = 100+(50-10) + V+III = 148. What on earth is confusing about that?
[*] FOUR + ONE = FIVE because FOUR = (FIVE – ONE) and so (FIVE -ONE) + ONE = FIVE. The -ONE and +ONE cancel. IV +I = IVI, THe I’s before and after cancel. Other example: LXIV +XCVII = XCLXIVVII. The Xs one each side of CL cancel and single I on each side of VV cacel so = CLVVI. The VV combine to X and =CLXI. In other words 64 + 97 = (50+10 + (5-1)) + (100-10 + 5 + 2) = 100+50 + 5+5 + 1 = 100 + 50 + 10 +1 =161. Simple.
I dunno though. Dark Side of the Horse set it’s own level for sight puns that simply having 3 = square root of 9 and that’s a nerdy thing so we have a sheep in glasses, and a roman sheep leading a legion of arbitrarily 148 sheep just doesn’t seem to cut it. Unless there is some significance to 148.
Although there are semantic rules of cleaning and not going exceeding magnitudes in subtraction…
Woozy, yes, these are interesting to contemplate. I like some awkward examples that eschew even single subtractions, and will show four of a kind for some symbols. Going the other direction, it is disconcerting to see someone (mostly moderns) try to subtract across multi levels. The recent practical occasion for needing to try this out was of course the year 1999. Would you accept “IMM”? Or maybe “MIM”? Many stuck with “MCMXCIX”.
heres what I should have said.
VI is ONE after FIVE. So that is obviously SIX.
And IV is ONE before FIVE. So that is obviously FOUR.
You will occasionally see in (in tarot cards mostly) VIIII for nine, and occasionally you will see on clocks IIX for eight.
Once the nineties occurred and we sometimes saw MCMXCIII I always figured the Cs cancel and it should be MXMIII but I guess some people think substraction should only be one degree of magnitude. I get it but ….
Actually in the early 2000s I saw a date MCMCI and I figured someone after a century of MCM + (I to XCIX) just couldn’t break the habit.
Mitch, I think those of us using digits would thing 19 = 20 -1 would first think 1999 could be IMM but psuedo romans would think 19=(10 + 10) – 1 = 10 + (10-1) and do MIM. Of course real romans think in magitudes and an 1999 = 1000 + 900 + 90 + 9 so MCMXCIX but from a calculating point of view those cross cancelinng C’s and X’s are …. wow.
I agree that he’s obviously counting sheep to fall asleep, that he’s doing it in an odd way, and that Roman numbers can be confusing. But I assumed there was some significance to CXLVIII or 148. If the point was that Roman numbers can be confusing, it would make sense if IV was followed by IVI or something. But even someone confused about Roman numbers wouldn’t try to follow IV with CXLVIII.
Fun fact (which I’m sure most of you already know): on clock faces that use Roman numerals, at least on the old ones, 4 is represented as IIII.
I sometimes use Roman numerals to impress my students with just how easy math can be, and how much harder it can be. I usually also point out that the numbers they’re used to are Arabic numerals, because Arabians came up with lots of clever stuff.
@ Chak – The reason they do that is not for mathematical simplicity (nine is always “IX”), but for visual symmetry: the width of the “IIII” on the right harmonizes better with the “VIII” (eight) on the left.
BTW, I got the Bliss/Martin book! Hefty physical book. Now to go relax and read …
“the numbers they’re used to are Arabic numerals, because Arabians came up with lots of clever stuff.”
They did come up with lots of clever stuff. But much of what we label “Arabic” is only because it came to Europe via Arabia. Positional representation of numbers was invented by Hindus in China and/or India.
Reading Woozy’s explanation of Roman numerals brought to mind this quote from Johann Sebastian Bach: “There’s nothing remarkable about it. All one has to do is hit the right keys at the right time and the instrument plays itself.”
If you have a chance, visit the “History of Philosophy (without any gaps)” website / podcasts / books. A now-concluded sequence within the still-ongoing main Western thread was “Philosophy in the Islamic World” which was quite an eye-opener for me. https://historyofphilosophy.net/series/islamic-world
Becky/woozy: I started to write something about how Roman numeral rules are not straightforward or obvious, but then gave up, because how do you convince someone that rules they think are obvious are not obvious?
Webb (Gordon Ramsey): “[Cooking this dish is easy.] It’s just local ingredients, simply cooked.”
Mitchell: “By you! King Lear is just English words put in order.”
I think I’ve mentioned this before, but I used to be a math major, and we did actually have conversations like this: “This step is trivial/obvious.” “I’m not sure, it is really obvious?” [Half an hour of consulting definitions, sketching proofs, etc. . .] “Oh yes, it is obvious, I see it now.”
If he jumps (!) from 4 to 148, it’s because the next 144 (=12*12) sheep come in a flock/legion instead of one by one, as is customary.
Now I can’t remember where, but I was going to bring up exactly this joke a couple days ago! Well, my version has the instructor / lecturer at the board say “This step is obvious … wait a minute ..” and check for several boards worth of space and most of the remaining time, to finally conclude “Yes, it is obvious”.
Oh now I remember! It was when everybody was yelling at me for calling the Frog Applause pun “straightforward”. I was ready to try to prove it! 🙂
Interesting discussion, but I think dvandom had it at the first comment. I can relate to going to sleep peacefully and then the mind takes over.
“All one has to do is hit the right keys at the right time and the instrument plays itself.”
Rosenkrantz and Guildenstern would beg to differ:
Ham. I pray will you play vpon this pipe? Ross. Alas my lord I cannot. Ham. Pray will you. Gil. I haue no skill my Lord. Ham. Why looke, it is a thing of nothing,
T’is but stopping of these holes,
And with a little breath from your lips,
It will giue most delicate musick. Gil. But this cannot wee do my Lord. Ham. Pray now, pray hartily, I beseech you. Ros. My lord wee cannot. (me? Ham. Why how vnworthy a thing would you make of
You would seeme to know my stops, you would play vpon [G1]
You would search the very inward part of my hart, mee,
And diue into the secreet of my soule.
Zownds do you thinke I am easier to be pla’yd
On, then a pipe? call mee what Instrument
You will, though you can frett mee, yet you can not
Play vpon mee, besides, to be demanded by a spunge.
And I thought: Why does Shrug’s copy of Tom Stoppard have the dialogue in such old-fashioned spellings?
But roman numerals are easy.
To read them: I = 1; V=5, X=10; L=50;C=100;D=500; M=1000 and putting an overline increases a symbol by a magnitude of a thousand. They are list higher left to right by highest denominations first and you add them up. Because they are listed highest to lowest if you ever do see a lower denomination before a higher denomination that means the lower denomination is subtracted.
So CXLVIII = 100 + (50-10) + 5 + 3=148
That’s it!
To write them there some intuitive but hard, but not too hard, to formulize rules. If you can use larger denominations do so (Represent 150 and $CL and not LLL or CXXXXVV because the largest block you can use is C so you must use it). The primary units are I, X,C, M of magnitudes 1, 10,100,1000. V,L,D are “half units” magnitude 5x 1, 5x 10, 5x 100. Their purpose of existence is to allow us to represent five to nine units of a magnitude in fewer terms. To allow us even fewer terms placing a primary unit if the magnitude immediately less then the current primary or half unit, to the left of a unit (so we can think of it as subtraction) allows for us to express $4$ or $9$ of the lesser unit.
If he jumps (!) from 4 to 148, it’s because the next 144 (=12*12) sheep come in a flock/legion instead of one by one, as is customary.
And for me that’s the missing step!
If a legion is 12 x 12 rather than the 10x 10 as I assumed and if Horace is keeping a running tally (which hadn’t occurred to me but is clear in hind sight that he would be) then that explains the 148.
And that is enough to make a joke (whereas an arbitrary roman numeral would not).
But that’s gross!
Yes, I agree that if Roman legions came in groups of 12*12 that would make the joke make sense. But Olivier, is that actually the case, or were you just speculating that they might come in that size? I didn’t find any indication that that was a standard Roman legion size with a quick search.
According to a handy dictionary, a Roman legion was “A division of from 3000 to 6000 men (including cavalry) in the Roman army”.
Interesting article relating to Roman numerals and mathematics, and how the Roman numeral notations had changed.
I don’t think the “148” that Samson picked has any “meaning”: it was probably just selected to make the number sufficiently complex, without being unreasonably large. As noted above, it is far too small for a “legion”, but also too large for the “century” that a “centurion” would command. The size of these “platoons” varied considerably (from 30 to 80, depending on the era), but never reached 100, let alone 144 soldiers.
P.S. @ WW – Back in college, one alleged strategy for solving math problems was to work down from the top equation, then work up from what the solution was known to be, and then write in the middle (between the two parts): “…it is thus intuitively obvious that…”
P.P.S. One guy who actually tried this trick got a note back from the T.A. that said “It is to me, but I don’t think it was to you.” (with points deducted).
Still trying to figure out if 148 has any significance here, or if it’s just a number that’s comically complicated to express in Roman numerals. I like the “144 more” idea but I don’t know if that’s a specific Roman unit size either.
Re: clocks with IIII for 4: I was always told that it was a superstitious avoidance of the letters “IV” which could refer to IVPPITER. Seems to be an urban legend, since the “subtractive” notation appears to be a medieval innovation that didn’t come along until centuries after anyone cared about Jupiter except perhaps as a planet.
A baker’s dozen is thirteen; a regular dozen with one more.
A gross is 144; a dozen dozens.
So what is a baker’s gross?
Answer: chicken guts in the doughnuts.
Kilby: I suspect that explicitly writing “it’s intuitively obvious,” or “it trivially follows” is actually more likely to call the T.A.’s attention to that line, and make them question if you know what you’re doing, than just saying “therefore” or “it follows.”
Yes, and I think we’re onto something with these thoughts about “a gross”.
All right, he’s asleep or hypnagogic, and logic is reduced. So the appearance of Roman soldiers ties into the Roman numerals, but doesn’t oblige the narrative to make them a legion or a century or anything Roman. Instead, Horace reverts to his sometimes business persona, and puts in an order for a common commercial measure of additional sheep, one gross. They are arriving in one bunch, and his running total reaches the number shown.
There we are, Cello! Sorry, I meant Viola! Sorry, I meant Wah-La!
On “Obvious” — At one time I worked for the Post Office. We trainees were given overviews of some matters we might or might not be dealing with on a daily basis, including various regulations. One set of rules was about how the station and individual carriers and mail handlers needed to treat various kinds of mail. Some important rules were about First Class mail of course. A different set protected Third, or Parcels, “of obvious value”.
Mailrooms and shippers knew all about postal regs. To make sure their Third Class and Parcel mail was handled safely and promptly, they wanted to ensure these pieces would count as being “of obvious value”. Some of them had a big rubber stamp (standard issue from stationery stores) and marked their mail .. wait for it … no not “VALUABLE” which you’d think would make it obvious … but instead “OBVIOUS VALUE”.
So this discussion has made me realize that you can mathematically prove that an MD is worth more than a JD:
MD = 1500
JD = ID = 499
QED
Since we’re 41 comments in with no clear explanation of why 148 specifically was chosen, I’m guessing that it’s just a randomly chosen number. If it was another comic, I would have accepted that much sooner, but with Dark Side of the Horse I have more of an expectation of an “Aha!” insight after a potentially very long wait.
So you don’t accept the “got to IV by single counting, then ordered another gross from the sheep supply — 4 + 144 = 148 = CXLVIII”?
Oh, sorry, I actually thought you were joking! 😮
That seems pretty convoluted to me. There’s no sign that he’s resorting to a business persona, and why would the 144 sheep that he ordered be carrying a Roman banner (and wearing uniforms, I think)? I think it’s more likely that this is just a bunch of Roman sheep following their leader, and that 144 is just a randomly chosen large number.
” If it was another comic, I would have accepted that much sooner, but with Dark Side of the Horse I have more of an expectation of an “Aha!” insight after a potentially very long wait.”
Exactly!
“Oh, sorry, I actually thought you were joking!”
Me too but I thought he was joking about stuffing donuts down his pants too.
larK says: So this discussion has made me realize that you can mathematically prove that an MD is worth more than a JD: MD = 1500 JD = ID = 499
But with that prompt we cannot forget to remind everyone of the famous point that Halloween and Christmas are just notational variants:
31 OCT == 25 DEC
The problem with Roman legions is that their composition has varied throughout history.
Roughly, one legion is made of 10 cohorts, each cohort holds 3 or 4 maniples comprising 120 to 160 men. One maniple is 2 centuries.
In the Straight Dope article, they mentioned sundials. Indeed, examples of ancient Roman sundials did use IIII so it’s possible that early clock makers copied that style.
Following from Olivier’s hint:
For IV we have one centurion. That might be followed by two centurions. Instead, we have 148. A common size of a maniple (two centuries of 80) is 160. In the earlier panels, we have 1 + 2 + 9 = 12, which combined with 148 makes a those two centuries (instead of two centurions).
Q.E.D. Simple and straightforward 🙂
A more interesting question to ask would be whether there is some significance to 148 in Finland, the cartoonist’s home country.
Q.E.D. Simple and straightforward
Intuitively obvious to the most casual observer. And they don’t get much more casual than this observer, amiright people?
Comics I Don't Understand 
He tries counting sheep to fall asleep, as per cliche, but his mind won’t shut off and he starts free-associating. Square root of nine for three, then IV for four…which leads to a centurion sheep leading a full unit.
That looks like more than just one unit, if the “148” is an accurate count of the “flock”.
My favorite rock concert album and video were “Velvet Underground Live MCMXCIII”. Which devotees know to say aloud as “em cee em ex cee aye-aye-aye”.
You know what year that was done, too.
In the first panel, it’s clear he’s counting sheep to get to sleep.
In the second panel, you see the square root of 9 (which is 3). Here’s where the reader sees that more creative ways of counting are being introduced.
The third panel has two parts: The first part shows “IV” (the Roman numeral for 4). Along with the sheep in Roman regalia, this goes along with the trope introduced in the second panel, in that more creative ways of counting are being used.
But then there’s the third panel’s second part: “CXLVIII” and it being represented with a legion of sheep in Roman soldier garb. That’s kind of confusing, so what’s that all about?
I think it’s just a visual pun that showcases the difficulty of Roman numerals. Let’s face it, once you get to “IV” (I plus V is… 4?) things get a little wonky in the Roman world of numbers. (What’s after “IV”? IV + I, right? So, “IVI”?) And if “IV” isn’t confusing enough for you, I’m sure that “CXLVIII” certainly is.
Personally, I think that the strip would be slightly clearer if the “IV” sheep was placed in its own separate panel (the third panel), and the “CXLVIII” sheep were placed in the final fourth panel. That way, the creativeness of counting sheep is established in the first three panels, and the confusion of Roman numerals is kept separate in the fourth panel.
In case any reader here is relatively unfamiliar with the Dark Side of the Horse comic, the “counting sheep to fall asleep” trope is one of those he reuses frequently and takes joy in twisting into unexpected variants. Maybe second only to “elevator triangular call buttons” and slightly ahead of “highway roadside hazard warning signs”.
Most kids learn Roman numerals in school, but my knowledge of them was perfected by watching “Looney Tunes” every Saturday morning. Even as kids, we observed that the copyright date in the opening credits was a fairly reliable indicator for the quality of the upcoming cartoon. The best ones were dated 1951-53 (MCMLI to LIII), anything before that was usually too corny, and anything 1956 or later was usually garbage (with some notable exceptions).
P.S. Chuck Jones was the most reliable director, but an even more reliable indicator were stories written by Michael Maltese.
P.S. @ J-L – There are some exceptions, but DSotH is almost always a three-panel strip.
” Let’s face it, once you get to “IV” (I plus V is… 4?) things get a little wonky in the Roman world of numbers. (What’s after “IV”? IV + I, right? So, “IVI”?) And if “IV” isn’t confusing enough for you, I’m sure that “CXLVIII” certainly is.”
Um…. no…. I always considered Roman Numerals to be very straight forward, a number to the left of a larger means to subtract from so IV must be read as V- I which is ….. 4? well, yeah….. and IVI = V-I+I=V. Although there are semantic rules of cleaning and not going exceeding magnitudes in subtraction… such thinking is useful if you try to add/subtract/multiply roman numerals without decimal conversion[*].
And CXLVIII = 100+(50-10) + V+III = 148. What on earth is confusing about that?
[*] FOUR + ONE = FIVE because FOUR = (FIVE – ONE) and so (FIVE -ONE) + ONE = FIVE. The -ONE and +ONE cancel. IV +I = IVI, THe I’s before and after cancel. Other example: LXIV +XCVII = XCLXIVVII. The Xs one each side of CL cancel and single I on each side of VV cacel so = CLVVI. The VV combine to X and =CLXI. In other words 64 + 97 = (50+10 + (5-1)) + (100-10 + 5 + 2) = 100+50 + 5+5 + 1 = 100 + 50 + 10 +1 =161. Simple.
I dunno though. Dark Side of the Horse set it’s own level for sight puns that simply having 3 = square root of 9 and that’s a nerdy thing so we have a sheep in glasses, and a roman sheep leading a legion of arbitrarily 148 sheep just doesn’t seem to cut it. Unless there is some significance to 148.
Although there are semantic rules of cleaning and not going exceeding magnitudes in subtraction…
Woozy, yes, these are interesting to contemplate. I like some awkward examples that eschew even single subtractions, and will show four of a kind for some symbols. Going the other direction, it is disconcerting to see someone (mostly moderns) try to subtract across multi levels. The recent practical occasion for needing to try this out was of course the year 1999. Would you accept “IMM”? Or maybe “MIM”? Many stuck with “MCMXCIX”.
heres what I should have said.
VI is ONE after FIVE. So that is obviously SIX.
And IV is ONE before FIVE. So that is obviously FOUR.
You will occasionally see in (in tarot cards mostly) VIIII for nine, and occasionally you will see on clocks IIX for eight.
Once the nineties occurred and we sometimes saw MCMXCIII I always figured the Cs cancel and it should be MXMIII but I guess some people think substraction should only be one degree of magnitude. I get it but ….
Actually in the early 2000s I saw a date MCMCI and I figured someone after a century of MCM + (I to XCIX) just couldn’t break the habit.
Mitch, I think those of us using digits would thing 19 = 20 -1 would first think 1999 could be IMM but psuedo romans would think 19=(10 + 10) – 1 = 10 + (10-1) and do MIM. Of course real romans think in magitudes and an 1999 = 1000 + 900 + 90 + 9 so MCMXCIX but from a calculating point of view those cross cancelinng C’s and X’s are …. wow.
I agree that he’s obviously counting sheep to fall asleep, that he’s doing it in an odd way, and that Roman numbers can be confusing. But I assumed there was some significance to CXLVIII or 148. If the point was that Roman numbers can be confusing, it would make sense if IV was followed by IVI or something. But even someone confused about Roman numbers wouldn’t try to follow IV with CXLVIII.
Fun fact (which I’m sure most of you already know): on clock faces that use Roman numerals, at least on the old ones, 4 is represented as IIII.
I sometimes use Roman numerals to impress my students with just how easy math can be, and how much harder it can be. I usually also point out that the numbers they’re used to are Arabic numerals, because Arabians came up with lots of clever stuff.
@ Chak – The reason they do that is not for mathematical simplicity (nine is always “IX”), but for visual symmetry: the width of the “IIII” on the right harmonizes better with the “VIII” (eight) on the left.
BTW, I got the Bliss/Martin book! Hefty physical book. Now to go relax and read …
“the numbers they’re used to are Arabic numerals, because Arabians came up with lots of clever stuff.”
They did come up with lots of clever stuff. But much of what we label “Arabic” is only because it came to Europe via Arabia. Positional representation of numbers was invented by Hindus in China and/or India.
Reading Woozy’s explanation of Roman numerals brought to mind this quote from Johann Sebastian Bach: “There’s nothing remarkable about it. All one has to do is hit the right keys at the right time and the instrument plays itself.”
If you have a chance, visit the “History of Philosophy (without any gaps)” website / podcasts / books. A now-concluded sequence within the still-ongoing main Western thread was “Philosophy in the Islamic World” which was quite an eye-opener for me. https://historyofphilosophy.net/series/islamic-world
Becky/woozy: I started to write something about how Roman numeral rules are not straightforward or obvious, but then gave up, because how do you convince someone that rules they think are obvious are not obvious?
Mitchell and Webb’s Kitchen Nightmares @1:37:
Webb (Gordon Ramsey): “[Cooking this dish is easy.] It’s just local ingredients, simply cooked.”
Mitchell: “By you! King Lear is just English words put in order.”
I think I’ve mentioned this before, but I used to be a math major, and we did actually have conversations like this: “This step is trivial/obvious.” “I’m not sure, it is really obvious?” [Half an hour of consulting definitions, sketching proofs, etc. . .] “Oh yes, it is obvious, I see it now.”
If he jumps (!) from 4 to 148, it’s because the next 144 (=12*12) sheep come in a flock/legion instead of one by one, as is customary.
Now I can’t remember where, but I was going to bring up exactly this joke a couple days ago! Well, my version has the instructor / lecturer at the board say “This step is obvious … wait a minute ..” and check for several boards worth of space and most of the remaining time, to finally conclude “Yes, it is obvious”.
Oh now I remember! It was when everybody was yelling at me for calling the Frog Applause pun “straightforward”. I was ready to try to prove it! 🙂
Interesting discussion, but I think dvandom had it at the first comment. I can relate to going to sleep peacefully and then the mind takes over.
“All one has to do is hit the right keys at the right time and the instrument plays itself.”
Rosenkrantz and Guildenstern would beg to differ:
Ham. I pray will you play vpon this pipe?
Ross. Alas my lord I cannot.
Ham. Pray will you.
Gil. I haue no skill my Lord.
Ham. Why looke, it is a thing of nothing,
T’is but stopping of these holes,
And with a little breath from your lips,
It will giue most delicate musick.
Gil. But this cannot wee do my Lord.
Ham. Pray now, pray hartily, I beseech you.
Ros. My lord wee cannot. (me?
Ham. Why how vnworthy a thing would you make of
You would seeme to know my stops, you would play vpon [G1]
You would search the very inward part of my hart, mee,
And diue into the secreet of my soule.
Zownds do you thinke I am easier to be pla’yd
On, then a pipe? call mee what Instrument
You will, though you can frett mee, yet you can not
Play vpon mee, besides, to be demanded by a spunge.
And I thought: Why does Shrug’s copy of Tom Stoppard have the dialogue in such old-fashioned spellings?
But roman numerals are easy.
To read them: I = 1; V=5, X=10; L=50;C=100;D=500; M=1000 and putting an overline increases a symbol by a magnitude of a thousand. They are list higher left to right by highest denominations first and you add them up. Because they are listed highest to lowest if you ever do see a lower denomination before a higher denomination that means the lower denomination is subtracted.
So CXLVIII = 100 + (50-10) + 5 + 3=148
That’s it!
To write them there some intuitive but hard, but not too hard, to formulize rules. If you can use larger denominations do so (Represent 150 and $CL and not LLL or CXXXXVV because the largest block you can use is C so you must use it). The primary units are I, X,C, M of magnitudes 1, 10,100,1000. V,L,D are “half units” magnitude 5x 1, 5x 10, 5x 100. Their purpose of existence is to allow us to represent five to nine units of a magnitude in fewer terms. To allow us even fewer terms placing a primary unit if the magnitude immediately less then the current primary or half unit, to the left of a unit (so we can think of it as subtraction) allows for us to express $4$ or $9$ of the lesser unit.
So 148 = 100 + 4×10 + 8×1 = 100 + (5×10-10) + 5×1 + 3x 1 = C + XL + VIII= CXLVIII.
And for me that’s the missing step!
If a legion is 12 x 12 rather than the 10x 10 as I assumed and if Horace is keeping a running tally (which hadn’t occurred to me but is clear in hind sight that he would be) then that explains the 148.
And that is enough to make a joke (whereas an arbitrary roman numeral would not).
But that’s gross!
Yes, I agree that if Roman legions came in groups of 12*12 that would make the joke make sense. But Olivier, is that actually the case, or were you just speculating that they might come in that size? I didn’t find any indication that that was a standard Roman legion size with a quick search.
According to a handy dictionary, a Roman legion was “A division of from 3000 to 6000 men (including cavalry) in the Roman army”.
Interesting article relating to Roman numerals and mathematics, and how the Roman numeral notations had changed.
https://washingtoncitypaper.com/article/191885/how-did-anyone-do-math-in-roman-numerals/
I don’t think the “148” that Samson picked has any “meaning”: it was probably just selected to make the number sufficiently complex, without being unreasonably large. As noted above, it is far too small for a “legion”, but also too large for the “century” that a “centurion” would command. The size of these “platoons” varied considerably (from 30 to 80, depending on the era), but never reached 100, let alone 144 soldiers.
P.S. @ WW – Back in college, one alleged strategy for solving math problems was to work down from the top equation, then work up from what the solution was known to be, and then write in the middle (between the two parts): “…it is thus intuitively obvious that…”
P.P.S. One guy who actually tried this trick got a note back from the T.A. that said “It is to me, but I don’t think it was to you.” (with points deducted).
Still trying to figure out if 148 has any significance here, or if it’s just a number that’s comically complicated to express in Roman numerals. I like the “144 more” idea but I don’t know if that’s a specific Roman unit size either.
Re: clocks with IIII for 4: I was always told that it was a superstitious avoidance of the letters “IV” which could refer to IVPPITER. Seems to be an urban legend, since the “subtractive” notation appears to be a medieval innovation that didn’t come along until centuries after anyone cared about Jupiter except perhaps as a planet.
https://www.straightdope.com/21341605/why-do-clocks-with-roman-numerals-use-iiii-instead-of-iv
A riddle my uncle used to like:
A dozen is twelve.
A baker’s dozen is thirteen; a regular dozen with one more.
A gross is 144; a dozen dozens.
So what is a baker’s gross?
Answer: chicken guts in the doughnuts.
Kilby: I suspect that explicitly writing “it’s intuitively obvious,” or “it trivially follows” is actually more likely to call the T.A.’s attention to that line, and make them question if you know what you’re doing, than just saying “therefore” or “it follows.”
Yes, and I think we’re onto something with these thoughts about “a gross”.
All right, he’s asleep or hypnagogic, and logic is reduced. So the appearance of Roman soldiers ties into the Roman numerals, but doesn’t oblige the narrative to make them a legion or a century or anything Roman. Instead, Horace reverts to his sometimes business persona, and puts in an order for a common commercial measure of additional sheep, one gross. They are arriving in one bunch, and his running total reaches the number shown.
There we are, Cello! Sorry, I meant Viola! Sorry, I meant Wah-La!
On “Obvious” — At one time I worked for the Post Office. We trainees were given overviews of some matters we might or might not be dealing with on a daily basis, including various regulations. One set of rules was about how the station and individual carriers and mail handlers needed to treat various kinds of mail. Some important rules were about First Class mail of course. A different set protected Third, or Parcels, “of obvious value”.
Mailrooms and shippers knew all about postal regs. To make sure their Third Class and Parcel mail was handled safely and promptly, they wanted to ensure these pieces would count as being “of obvious value”. Some of them had a big rubber stamp (standard issue from stationery stores) and marked their mail .. wait for it … no not “VALUABLE” which you’d think would make it obvious … but instead “OBVIOUS VALUE”.
So this discussion has made me realize that you can mathematically prove that an MD is worth more than a JD:
MD = 1500
JD = ID = 499
QED
Since we’re 41 comments in with no clear explanation of why 148 specifically was chosen, I’m guessing that it’s just a randomly chosen number. If it was another comic, I would have accepted that much sooner, but with Dark Side of the Horse I have more of an expectation of an “Aha!” insight after a potentially very long wait.
So you don’t accept the “got to IV by single counting, then ordered another gross from the sheep supply — 4 + 144 = 148 = CXLVIII”?
Oh, sorry, I actually thought you were joking! 😮
That seems pretty convoluted to me. There’s no sign that he’s resorting to a business persona, and why would the 144 sheep that he ordered be carrying a Roman banner (and wearing uniforms, I think)? I think it’s more likely that this is just a bunch of Roman sheep following their leader, and that 144 is just a randomly chosen large number.
” If it was another comic, I would have accepted that much sooner, but with Dark Side of the Horse I have more of an expectation of an “Aha!” insight after a potentially very long wait.”
Exactly!
“Oh, sorry, I actually thought you were joking!”
Me too but I thought he was joking about stuffing donuts down his pants too.
larK says:
So this discussion has made me realize that you can mathematically prove that an MD is worth more than a JD:MD = 1500JD = ID = 499But with that prompt we cannot forget to remind everyone of the famous point that Halloween and Christmas are just notational variants:
31 OCT == 25 DECThe problem with Roman legions is that their composition has varied throughout history.
Roughly, one legion is made of 10 cohorts, each cohort holds 3 or 4 maniples comprising 120 to 160 men. One maniple is 2 centuries.
In the Straight Dope article, they mentioned sundials. Indeed, examples of ancient Roman sundials did use IIII so it’s possible that early clock makers copied that style.
Following from Olivier’s hint:
For IV we have one centurion. That might be followed by two centurions. Instead, we have 148. A common size of a maniple (two centuries of 80) is 160. In the earlier panels, we have 1 + 2 + 9 = 12, which combined with 148 makes a those two centuries (instead of two centurions).
Q.E.D. Simple and straightforward 🙂
A more interesting question to ask would be whether there is some significance to 148 in Finland, the cartoonist’s home country.
Q.E.D. Simple and straightforward
Intuitively obvious to the most casual observer. And they don’t get much more casual than this observer, amiright people?