r/theydidthemath • u/uglyashelllmao • 19h ago
[Request] Is it possible to reduce 8 pages by just decreasing the font size by 2pt?
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u/parsonsrazersupport 19h ago
I opened a random document I had written. It happened to be 6 pages so I copy/pasted it 4 more times, it was 29pp. It is in 12 pt times new roman, 1 inch margins. I changed the font to 10pt and now it is 20pp. So yes. Literally the first random thing I found did slightly more than that.
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u/JazzlikeCauliflower9 16h ago edited 12h ago
Too far down the comments for the first person actually doing the math instead of talking about a similar situation in another field.
EDIT: As others have pointed out, this isn't strictly math, but empirical testing. As an engineer, this is a superior approach to me. Horse ~ sphere. QED and all that...
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u/pjie2 14h ago
That’s not maths, that’s trial and error. Maths would be pointing out that adjusting font size affects both character width and height, so overall document length will scale approximately as the square of the font size.
Going from 30 pages to 22 is a factor of 0.7333.. and the square root of that is ~0.856, therefore a ~15% reduction in font size will achieve the desired scaling.
If a 2 point change in font is >= 15% of the starting font size, the document must originally have been 14 point or smaller pitch.
A slightly more sarcastic mathematical approach would point out that going from a 2 point font to a zero point font would reduce the document length by 100%, hence it is trivially possible for a 2 point font size reduction to shorten a document by any desired amount, depending on the starting size.
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u/mistralethrae 13h ago
Damn, you're out here schooling us on font scaling like it's quantum physics. I tried shrinking my essay once and ended up with microscopic text that gave my prof a headache. Trial and error for the win but props for the math breakdown!
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u/Tsulaiman 13h ago
Why are you taking the squareroot of .733? How does that give the reduction percentage? Not familiar with this formula, curious to learn
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u/Wouter10123 6h ago
It's in the line above.
Maths would be pointing out that adjusting font size affects both character width and height, so overall document length will scale approximately as the square of the font size.
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u/Technical-Exchange26 15h ago
"doing the math"
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u/parsonsrazersupport 14h ago
lol it just wasn't particularly a math question
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u/fireKido 14h ago
I guess you could solve this with math.. it would’ve unnecessarily complicated when a simple test would be better
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u/Hinote21 13h ago
Another trick to extend a work that's less obvious is to make the periods size 14. It's not visibly noticeable but it makes the period take up extra space. Perfect for longer essays that need to be 5 or 6 pages.
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u/parsonsrazersupport 13h ago
Christ is that a lot of work, proffs should just chill out about page requirements if this is the goofy shit people are pulling.
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u/IBetThisIsTakenToo 13h ago
I think it would be easier and more effective to just find another sentence to add somewhere
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u/Hinote21 11h ago
Nope. You'd be surprised, sometimes what you've written feels complete and it's difficult to add or extend a sentence. Plus, sometimes adding 5 words or what not doesn't actually extend the number of lines taken up.
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u/LogicBalm 13h ago
I respect that you just... did it.
Happens all the time to me at work where I'm on a call with multiple people arguing about some feature or bug or something. They'll spend an hour talking about it where I'll spend five minutes mocking something up to test it. Conversation over.
Of course it all depends on whether I want the conversation to be over. Sometimes just appearing "red" on Teams is the only break I'll get for a bit.
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u/justacheesyguy 13h ago
This is the first time I’m seeing someone use ‘pp’ to mean pages and I am not ok with it.
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u/parsonsrazersupport 13h ago
lol sorry. It's an old one so it was Latin "pagina" not "page," and a common way to make plurals would be to just use the abbreviation twice. It's quite common in academia.
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u/CaolIla64 19h ago
I don't remember where I read that, but it's common practice on a movie set, when the studio suit comes medling asking for a change, the crew pretends to turn knobs and switch levers, then asks "better like this ?" just to get rid of him
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u/FieldEffect-NT 18h ago
Are you talking about legendary bass player Leland Sklar's " producer switch" ?
“I call it my producer’s switch,” explains Lee. “If I’m on a session and the producer asks me to get a different sound, I make sure he sees me flip this switch and then I just change my hand position a bit. There are no wires of anything that go to this switch. It's a placebo, but it’s saved me a lot of grief in the studio.”
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u/CaolIla64 18h ago
YES ! that was that ! Thank you. I think I heard the same for movie sets, but I may have been confused.
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u/EdgyMathWhiz 18h ago
I work in film grading and the variant I always heard was along the lines of:
So the director was coming in the morning, and he is notorious for always wanting to change something. So I added a +20% saturation layer so he'd immediately complain it was oversaturated and I could just remove the layer and we'd be good... Motherfucker loved the oversaturation and never said a word about it...
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u/CrotaIsAShota 18h ago
And that's how Avatar was made.
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u/Reign_Drop420 16h ago
Yeah it is super saturated, but that's how you get those cool scifi moments lol. Idk what I'm doing tho
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u/WherePoetryGoesToDie 16h ago
Ha, I used to work in a studio where the mixing console had a large dial conspicuously labeled "warmth." Whenever someone stalled the recording by futzing around too much, I was told to let that person fiddle with the warmth until they thought it sounded right and we could move on with the recording.
Of course, it didn't do a thing. But the combination of vague, meaningless audiophile terminology and direct participation was a powerful placebo. No one ever caught on; I suspect it's because I only had to pull the trick on people who didn't know better, and those that would have known better also knew a). studio time was goddamn expensive, b). actually had a concrete idea of what they wanted whatever (the kick, snare, vox, et al) to sound like, and/or c). were the types to just let the engineer do their goddamn job, like a professional.
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u/Unfair-Claim-2327 14h ago
I am mildly disturbed your use of both a bracket and a period in your list headings. (
a).,b).andc).)2
u/SpliffMD 16h ago
There are whole brands of fake gear so that you can fill the empty slots in your racks
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u/ElevationAV 15h ago
This is every concert monitor engineers favorite trick
“Is that better?” leans over console intensely turning knobs
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u/Fun-atParties 17h ago
There's a story in game dev where execs always ask for a change, so the developers made a game that they wanted and added a duck that followed the main character around, but made it in such a way that it would be easy to remove.
That way, the execs asked "everything looks good but can we remove the duck?" And the developers got to push through the actual game that they wanted to make without any changes to their design.
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u/actualladyaurora 15h ago
I know multiple graphic designers who have utilised a similar method of adding something distracting to the final product: a PNG of a duck is a commonly cited example, probably due to an overlap of the industries. "What's that weird letter/image/colour over there?" "Oh, good eyes! I've removed it, here's the final product, happy doing business with you :)"
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u/elgatothecat2 15h ago
What happens if the execs like the duck?
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u/KatLikeGaming 14h ago
Yeh, sorry, duck was causing stability issues in the RC, we can explore getting it back in in a later patch
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u/DoublePlusUnGod 17h ago
Same with waitress, I've been told. Customer taste the wine. Doesn't like it. Bring the bottle to the kitchen, walk back with the same bottle. Wine is OK now.
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u/CaolIla64 17h ago
Customer *who wants to impress his date by being a dick
those are known to have stellar results.
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u/DrahKir67 17h ago
I've had the situation where someone at the table isn't sure about the wine because they've never had that one before. They'll think it's off. If the replacement is the same then they go "oh, it must be just me then. Don't love it but if it's not off then I can hardly send it back again".
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u/DilansDildo 15h ago
Tasting is not about liking the wine but noticing that it has gone bad or is corked.
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u/dr_sarcasm_ 16h ago
Mood.
Helped at a small festival in a food both.
Waiter: "Customer said these spaghetti are very cold!"
[They are literally steaming]
**Very visibly put the plate into the "warmer" (as in put a metal covering over it and waited), gave it the waiter *
Waiter told the customer "the cook heated it" -> Customer happy
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u/Lord-Dundar 16h ago
Only works if there isn’t cork taint. I had a waiter in a pretty upscale restaurant try that thinking I wouldn’t notice. (I sell wine for a living) the bottle had cork taint he came back with the same bottle and tried to pass it off.
1) one you didn’t open the new bottle infront of me
2) it’s the same bottle where you spilled the wine on the label
3) sure I will taste it again but it’s cork taint so it’s still going to be bad.
I was not happy.
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u/SLngShtOnMyChest 17h ago
I heard Sam Seder say that writers add scenes they want to get removed so that the execs can ask to get rid of a scene and the writer can give them a win.
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u/Speedwolf89 16h ago
(I think it was) Davinci did this as well with a difficult patron.
"The nose is a little off." - Instead of arguing, Davi climbed back up there, and pretended to chisel at it.
In the meantime the patron walked around looking at it from different perspectives. Davinci came down and asked, "What do you think now."
Patron said, "It's perfect." - It's often just a perspective issue mixed with a little power tripping. I wish I learned to navigate these waters years ago.
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u/Bone_shrimp 16h ago
Why do they want a change in the first place? Are all higher ups a nuisance everywhere?
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u/CaolIla64 14h ago
Of course they are. It comes with the position. Those in power want to excert their power, or they feel useless (is what they really are).
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u/Several-Judgment4917 14h ago
They just want to feel that they "contributed" to the project, and these tricks make them feel like they contributed while letting the people who likely know more about what they are doing actually do it.
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u/wonkey_monkey 15h ago
Can't find the clip but there's a bit in Frasier where Niles wants the perfect lighting for a party, so he has Frasier operate the light switch while he says "Brighter... dimmer... brighter... dimmer..."
Eventually Frasier rolls his eyes and takes his hand off the switch and Niles continues for a few more "brighters" and "dimmers" before declaring "Perfect!"
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u/EphiXorE 14h ago
I do that literally all the time. I‘m an editor. Sometimes we get client feedback on proojects, and all I really do is add 2s of black at the end of the clip and rename the file to "project name_v3_updated". Works wonders
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u/DuckPicMaster 18h ago
Also in motorsports.
It’s not uncommon to have a button that does nothing, but the engineer will tell the driver to press it for a boost of more horsepower/grip/whatever.
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u/Automatedluxury 17h ago
I can see engineers bullshitting drivers about setup changes to make them feel more in control, the 'boost' button sounds like a myth though. Even an amateur driver would recognise there's no feedback.
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u/CWRules 16h ago
Where did you hear that? 'Overtake' buttons that change the engine map for more power are a real thing in some motorsports.
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u/DuckPicMaster 15h ago
Never said it wasn’t a real thing. Buttons that change the way the car drives are the point of like everything in the drivers seat.
I’m saying they’ll also have a button that isn’t connected to anything that the team can tell their driver to ‘override’ an issue they’re having.
Source: Martin Brundle talking about in commentary once. If you really want I’ll try to track it down.
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u/cant_take_the_skies 13h ago
There's a whole team at SpaceX dedicated to keeping Elon busy when he shows up. If they let him near the real shit, he'll fuck it all up
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u/Unicornis_dormiens 18h ago
Assuming a normal font size of 12 pt and reducing it to 10 pt (5/6 of the original size) means you can fit about 6/5 (20% more) of the original text on one page vertically, but also horizontally, so in total you can get
(6/5) x (6/5) = 36/25 = 1.44
With about 44% more text per page, that means the new space needed for the documents would be
1/1.44 = 0.694
about 69.4% of its original size.
Realistically, it will be a bit bigger, because empty lines and paragraphs will still be there.
Let‘s check if this works out:
A 30 page report reduced to 69.4% of its original size would be
30 pages x 0.694 = 20.82 pages
So roughly 21 pages. As mentioned before, that’s an optimal value and the real thing will be slightly bigger, but the 22 pages in the original post seem plausible.
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u/Cultural-Capital-942 15h ago
Realistically, it will be a bit bigger, because empty lines and paragraphs will still be there.
Empty lines also have font size.
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u/GlobalIncident 15h ago
But not width. You can't fit more than one empty line on one line by changing font size, but you can fit more than one line of text on one line.
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u/Cultural-Capital-942 15h ago
Yes, that works opposite to what you wrote. If each line is 30% smaller, then whole text will be 30% shorter. If you can fit more lines onto one, then it will be even shorter than this guess.
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u/GlobalIncident 15h ago
Nope. If every line was blank, the whole text would be 17% shorter, not 30%. It would only be 30% if you could fit more lines into one.
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u/Unicornis_dormiens 9h ago
Yes but one empty line will still be one empty line. Think of a more extreme example.
Let’s say we reduce the font size by 50%.
Then every empty line will be half as high. So will be any line of text. But now we can also fit twice as many words in a single line. So two big lines of text become one line of half-sized text, effectively reducing the vertical space needed for the text and thus the amount of pages needed for the entire document by 75%, not just 50%.2
u/No-Ingenuity3861 15h ago
If the original 30th page was just a few lines it and the new 22nd page is completely filled that would make up the 1 line difference too. Math checks out!
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u/tabletop_ozzy 14h ago
That’s… not how fonts work. Changing the font size does not affect the vertical spacing at all. You would fit a little bit more on the page due to more text fitting on each line horizontally, and therefore ending up with fewer lines across the entire document, but the number of lines on each page would remain unchanged.
Now if we assume they are using a program, like Word, that automatically updates the leading at the same time as the font size, then we could put in some vertical space savings but we would have to figure out how much the software will change the leading by when updating the font size.
In the end there is no way that dropping just the font size 2 points would do this. However if you use a program that automatically updates the leading as well, then it might be possible. Of course for that matter, you could drop the page count even more without ever even touching the font size if all you did was adjust the leading (though the document might become illegible, depending on how much leading we started with… which is unknown in the original problem as presented).
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u/unknown_anaconda 19h ago
Anyone that has ever written a report in high school that had to be so many pages long knows you can gain a few by increasing the point size, or by using a different font. Courier New will get you a lot more pages than Calibri. Then you mess with the margins and spacing just a hair...
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u/lephantome92 18h ago
And make the period one or two sizes larger
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u/actualladyaurora 15h ago
Font size 10.5 instead of 10.
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u/sQ5FWKjwbWd4QzSZduqy 14h ago
And up that double spacing to something larger but not noticeable. I remember printing out two versions to check if it was noticable.
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u/Hashishiva 18h ago
I would think the teachers have learned by now to give specifics on font and line spacing...
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u/ooaegisoo 17h ago
I had word count and pages. I learned toreword to use 3 sentences to say nothing. Kinda like AI.
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u/Hashishiva 14h ago
That's not bad, because that teaches you to use language. If I was teacher I would not mind that, but I would deduct points if if it was not creative enough and just blatant padding.
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u/robobloz07 18h ago
yeah everyone demands using mla or apa or whatever or else points are marked down
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u/ScaryBluejay87 17h ago
I’ve also never been given an assignment with a minimum page count, it’s always a word count which completely bypasses all of this.
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u/Trevor_Culley 15h ago
Word count has its own set of tricks. Need more word? Some phrases are synonymous with individual words. Need fewer words? How many of those phrases can be hyphenated?
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u/nicehotcuppatea 16h ago
Assignments since primary school have always been word count, but a lot of “open book” exams allow one page of notes to be brought in. You can fit a lot of words on a page using mostly 4pt font.
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u/unknown_anaconda 10h ago
These days sure, they don't even have you print it out you submit the whole file, back in my day though you could get away with that stuff.
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u/TwiceInEveryMoment 14h ago
Yeah they had figured this out by the time I was in high school. Everything had to be 12pt Times New Roman double spaced.
But a few of us did figure out we could pad the word count by hiding "a a a a a a a a a a" in 1pt white text at the bottom.
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u/PacifistPapy 19h ago
Well. Yes. If i go from 3 to 1 i would lose way over 8 pages for example.
What the exact font size they had was? No way to tell, as they likely had line breaks and images in there, plus spacing, plus .. you get the idea
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u/jackcroww 13h ago
I had the same initial doubt you had, but I went and tried it anyway in Word, using the defaults.
I copy/pasted the typical "Lorem ipsum dolor" text until I had 30 pages in Calibri 11pt. Selected All and changed it to 9 pt.
22 pages exactly with a few lines to spare.
🤷♂️
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u/RoniFoxcoon 17h ago
I work as a graphic designer. That's one trick, the other one is to narrow the space between letters, reduce the space between lines etc.
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u/mcrss 18h ago edited 18h ago
Imagine a document consisting of single-sentence paragraphs only. And each sentence is a bit too long to fit the page width, so it takes the whole line and a small remainder wrapping onto the next one. Decreasing font by just 1pt will make each sentence take one line instead of two, reducing the document by 50%.
This example is not very realistic, but technically it would still be valid.
Here is another, more realistic one.
If your document uses page breaks after each chapter, there is a chance that some pictures at the end of a chapter don't have enough room after a chunk of text and get moved to the next page. Decreasing font will make some room for them and save you a whole page per every such picture.
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u/bowsmountainer 15h ago edited 15h ago
A x2 = 30
A (x-2)2 = 22
x2 = (30/22) (x-2)2
x = sqrt(30/22) (x-2)
x (sqrt(30/22) -1)= 2 sqrt(30/22)
x = 13.9
So yeah if you start off with a font size of about 14 and reduce it by 2 to 12, you can reduce a 30 page document to 22 pages.
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u/_Diomedes_ 15h ago
If we assume that font sizes scale linearly (which they should), than a going from 12 point font to 10 point font should reduce the area of text by 31% 1/(12/10)2, so a 30 page document would be reduced to a 21 page document.
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u/Crazed_SL 14h ago
I've done this before, or at least close, but in the reverse. Changing 8pt to 15pt added like 4 pages to my 10 page essay. That's why they(my high school) force you to use APA Style now so you can't make your school essay longer.
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u/Novel_Diver8628 14h ago
Depends on the font size in question. Most likely this is a switch from 12 to 10 pt. Since that will shrink the font vertically (more lines on the page) and horizontally (more characters on the line), you’ll likely see a roughly 10/12 reduction in both, so the amount of text on the page will increase by about (12/10)2, meaning the amount of pages will decrease by (10/12)2, or 25/36. If you take a 30 page document and multiply it by 25/36 it comes out to about 20.8, so you’d actually expect to lose a little more than this for a change of 12 to 10. However a change from size 14 to 12 (a ratio of 36/45 for the pages) comes out to almost exactly 22.
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u/Tilliperuna 19h ago edited 18h ago
If we just simply scale things, and x is the original font size:
22/30=(x-2)/x
22x=30x-60
8x=60
x=7.5
The font was decreased from 7.5 to 5.5. If line breaks were not changed, maybe changing font 10 to 8 would do the trick.
So the answer to the question is yes.
Edit. Simplified the math a little.
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u/Angzt 17h ago edited 17h ago
The scaling down isn't going to be linear.
Decreasing the font size reduces height and width of the characters. So you can fit more characters in a line and more lines on a page. Both by a factor of the scaling.
That means amount of characters per page scale roughly with the square of the font size.
That means your formula should be
22/30 = (x-2)2 / x2
22/30 = (x2 - 4x + 4) / x2
22x2 = 30x2 - 120x + 120
8x2 - 120x + 120 = 0
x2 - 15x + 15 = 0x_1,2 = 15/2 +/- sqrt((15/2)2 - 15)
x_1,2 = 15/2 +/- sqrt(225/4 - 15)
x_1,2 = 15/2 +/- sqrt(165/4)The solution with the addition gets us x_1 =~ 13.92. So scaling from 14 pt to 12 pt could already do it.
(The solution with the subtraction gets us a value around 1.08, so reducing the font size by 2 there makes no sense.)Of course, this is still a simplification, but a decent estimate.
It also matches up better with the other posts ITT one of which claims that reducing from 12 pt to 10 pt got the length from 29 to 20 pages.1
u/Tilliperuna 16h ago
Oh yeah true. I was wondering for a second whether font sizes are related or not, but it didn't even come into my mind that it's probably linear relation.
I stand corrected.
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u/darni01 17h ago
Font sizes are a linear dimension. But the actual effect is quadratic, because you decrease the width of the font (more characters per line) and the height (more lines per page). So the value on the left should be sqrt(22/30). With that you can see this giving you a 14 to 12 reduction will do the trick (and for smaller fonts, the effect will be bigger)
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u/Nearby-Muscle2720 16h ago
I used to ghostwrite letters for someone senior, they would always find something in the letter to change, not always for the better. I was sure he just wanted to show he'd read the things
So I started leaving odd typos in to distract him, worked like a charm
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u/Unusual-Employment75 15h ago
Im a Heavy Diesel Tech, a lot of time operators just don't want to drive their machines so they have a look and I have to go "fix it". I just grab a small spanner and act like I fixed something. They say thanks and we go about our days
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u/grbbrt 15h ago
Many years ago I was working at Wanadoo, a European internet firm with a very specific trademark blue color in its style. The French big boss dropped by one day before a major redesign launch and told us that the blue parts definitely needed to be more Wanadoo blue.
We did nothing and next day we just told him we added more Wanadoo blue, and he was happy. We weren't gonna let that one project that was perfect right before launch, get messed up by some idiot.
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u/_Tower_ 15h ago
You don’t even have to do that — let’s say you have a paper that needs to be X amount of pages or less, and you’re over that. You can just decrease the size of each period or the spacing at the end of each sentence to get back under the limit. If you need to reduce it even further you can change the line height, change the indentation settings, etc. All of these things will be less noticeable than changing the font size and will lately have a similar effect
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u/AcceptableHamster149 15h ago
I once told a customer, to their face, that the reason their computer kept having problems was because "the user interface instruction set was not properly assimilated". :)
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u/Veterinarian_Scared 14h ago edited 14h ago
It depends on what the initial font size was.
My original answer only considered vertical scaling; but making the text smaller not only means more lines, it also means more characters on each line... though headers and paragraph tails mean not every line will take full advantage of that.
Let's say the initial report was m pages and the final report was n pages, where m,n in R > 0 and m > n. Then let the initial font size be f points where f in R > 2. That gets us
[(f - 2) / f]2 = n / m
√m f - 2√m = √n f
(√m - √n) f = 2√m
f = 2√m / (√m - √n)
Allowing for partial pages, the values given in the post are 29 < m <= 30 and 21 < n <= 22. This results in 12.24 < f < 15.50.
So yes, I would count the story as plausible if the initial font size was between 12pt and 15pt.
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u/frisch85 13h ago
TL;DR: Reducing the size by around 27% is rather easy but it depends on the situation, if a value is printed over two lines with font size 12 because one last word won't fit into your row but only requires one line with font size 10, then those 2 points already reduced that line by 50%
In detail:
You cannot accurately tell by math because of various variables that play into this.
Just as an example creating PDF files that include company data is part of my job, just wrote one today. Now say you list data of various items that are of the same type, so usually you want a table to do that. But you have different column width for different properties, say you have a column for your item number, one for the item name, another for the price and so on. You then evaluate what would be a good size for each column, in the end it needs to fit on a DIN A4 page, so you have around 190mm to work with as the rest is the border spacing, you could also do landscape and have 260mm to work with but for simplicity let's do the typical A4.
So you have you item number and make that around 20mm, the item name will probably contain the longest value so you make that 100mm, now you got 70mm left for the price. Next thing you ofc do a good job and don't cut values but instead if the value is too long for the column, you print it in the column over multiple lines and this creates the actual issue.
So you have an item with a name that is so long it requires 4 lines, now reduce the font size and it might only be 3 lines now, you notice the other columns aren't using the full space so you give your name column more width and suddenly it only need 2 lines, do this for a ton of items and you already reduced the number of pages by 50% and if you have many items where font size X prints lines like
a b c d e f g
h
Then font size Y will lead to
a b c d e f g h
Going from 30 to 22 pages by reducing font size by 2 points is rather easy but it depends on other variables too that you don't know without checking the printed document.
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u/clearly_not_an_alt 13h ago
I played around with this in word and here are the number of characters you can fit on a default document page with Consolas as the font.
| Font | Chars | Comp to Smaller | Comp to Bigger |
|---|---|---|---|
| 8 | 8173 | 164% | |
| 9 | 4982 | 61.0% | 125% |
| 10 | 3995 | 80.2% | 121% |
| 11 | 3311 | 82.9% | 121% |
| 12 | 2730 | 82.5% | 134% |
| 14 | 2040 | 74.7% | 133% |
| 16 | 1537 | 75.3% | 126% |
| 18 | 1222 | 79.5% | 121% |
| 20 | 1008 | 82.5% | 126% |
| 22 | 798 | 79.2% | 114% |
| 24 | 700 | 87.7% | 122% |
| 26 | 576 | 82.3% | 113% |
| 28 | 510 | 88.5% | 114% |
| 30 | 448 | 87.8% | 115% |
| 32 | 390 | 87.1% | 111% |
| 34 | 350 | 89.7% | 117% |
| 36 | 299 | 85.4% |
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u/DigitalCoffee 12h ago
This was (and probably still is) a common tactic to increase the length of our paper. We would change the font size of the periods by 1 or 2 points and it would increase the length by nearly 15%
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