Playing Lewis Carroll's Game of Logic on the ORIGINAL 150 YEAR OLD BOARD

Oxford Mathematician Dr Tom Crawford is joined by fellow KZbinr James Grime to play an original version of Lewis Carroll's Game of Logic. If only they can first deduce the rules...
Filmed at St Edmund Hall at the University of Oxford, where the book is located. Thanks to Heather the librarian for giving us access.
Produced by Dr Tom Crawford at the University of Oxford. Tom is Public Engagement Lead at the Oxford University Department of Continuing Education: www.conted.ox.ac.uk/profiles/...
Check out James' channel @singingbanana.
Watch Tom and James talk about their favourite pieces of Maths on @numberphile.
Read the book for yourself here: archive.org/details/gameoflog...
For more maths content check out Tom's website tomrocksmaths.com/
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
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[@andrewharing2637]

Watching two professors of mathematics struggle to work out that "No x are m " and "All y are m" means that no x are y has madw me feel much better about myself, thanks.

[@RomanQrr]

Oh! I have this book on my bookshelf! Game of Logic was my first step into understanding logical statements. So nice to see some of my favourite math KZbinrs showcase the book. I really recommend everyone to give it a read.

[@RomanQrr]

I will also say that the version I had used black and white stones instead of 0s and 1s in the illustrations, making it much easier to understand the rules.

[@uigrad]

Some important clarifications about the numbered compartments, and the 0's and 1's: The compartments are diagrammed on the very first page. Compartments 1-4 don't exist (I have no idea why). Compartments 5-8 are for the "small diagram" (when only x and y are shown). 5 is the top left (xy), 6 is the top right (xy'), 7 = bottom left (x'y), 8 = bottom right (x'y'). Compartments 9-16 are for the large diagram (with x, y, and m). They are in pretty much the same order as you read. So: 9 = xym', 10 = xy'm', 11 = xym, 12 = xy'm, 13 = x'ym, 14 = x'y'm, 15 = x'ym', 16 = x'y'm' In each compartment, you place a '0' (or gray marker / clouds) if you know nothing exists here. You place a '1' (or red marker / sun) for knowing that it definitely does exist. If you get a statement like "some dragons are uncanny", you have to realize that covers 2 different compartments (9 and 10), so you place the red marker on the border between these two compartments. If later you find that one of those compartments gets a gray, then you can slide the red marker fully into the other compartment. "All dragons are uncanny" can be separated into 2 parts: 1. Canny dragons do not exist (gray markers) 2. Some uncanny dragons do exist (red marker on a line between 2 compartments). It seems that the goal is to map out the statements on the large diagram first, then convert to the small diagram, and use that to draw your final conclusion. The variable 'm' is necessary to follow the logic, but it isn't used in the final conclusion! With these clarifications, it seems that the examples they give do work, although I haven't gone through every single one yet.

[@pbp6741]

Are we all yelling at the screen together?

[@fdagpigj]

yes, well except I don't literally yell at a screen when I'm alone at home with my microphone turned off

[@Schwuuuuup]

Man I'm riled up. I hate that I am so emotionally invested, that two random mathematicians are bad at logic

[@scragar]

@Schwuuuuup I don't think it's that they're bad at logic so much as the presentation and wording is unusual enough to cause confusion. Like the first time with the "some red apples are unwholesome" all that really said was "there's at least one red apple not in M", but the wording was interpreted to mean "some red apples are in M' and the rest must be in M", which really messed with the conclusion.

[@Schwuuuuup]

@@scragar don't take my comment too seriously they are obviously not bad a logic... But maybe they acted a bit narrow-minded and arrogant(?) ... what was hard to watch was when they did the mistakes over and over and believed that it must be typos instead of them failing to understand. "no one is in the house but whatwashisname" yes that means he is in the house... But not that he is having a toothache... But also not that he doesn't have a toothache . I guess what the explanation failed to convey (without putting the blame on anyone) is the meaning of 0="definitely not" and 1="guaranteed to have at least one case" and blank="unsure" . Arguing that the explanation is bad did not help the cause of understanding what was meant. It was NOT a language thing. I understood it and I'm not even a native speaker. But again, don't take it to seriously... We're just having some fun here

[@OneTrueBadShoe]

Yes! I was.

[@anash881]

It’s not a language issue - John is definitely in the house. It’s just that we don’t know if he has a toothache or not so therefore don’t have enough information to put a blue counter (or 1) in either square - in the absence of certainty, we leave the section blank. Think of the blue counters (1s) as certainties, the green counters (0s) as impossibilities and the blanks as maybes. The game becomes much easier when you work through the questions using these three states. The Venn diagram approach is only helpful when you know everything there is to know about the universe - but when there are gaps in the information I think it breaks down.

[@dalriada]

But the Venn diagram does help clarify what is a certainty, or an impossibility. The uncertainties can then be deduced.

[@thejackscraft3472]

It is a language issue if you consider the solution to be fully accurate, as it doesn't have a 0 in the top right section (John is outside the house), which would be impossible if John were definitely inside. so the maker does have a type somewhere, it's just a question of if it's in the situation posed, or the answer given.

[@hamed2800]

@@thejackscraft3472 the thing is either john has a toothache or he doesn't. putting blue counters means it's certainly true. so if you fill those two squares with blue counters then it would mean that john has a toothache and at the same time he doesn't have a toothache which is impossible. so we know one and only one of those two squares will be blue but we don't have enough info to know which one, so they should be left blank

[@thejackscraft3472]

@@hamed2800 I never said they shouldn't, I said that there is a language issue "if you consider the answer to be correct", since the language used in the problem has john definitely inside the house, but the answer distinctly doesn't. So if the answer is correct then the language used in the problem must be at fault for the discrepancy.

[@hamed2800]

​@@thejackscraft3472 you're right, I didn't notice your condition for it being language issue but I think the answer misses a 0 in the top outer right box and it is wrong, because "there's no one inside but john" really implies that john and only john is inside

[@SgtSupaman]

It didn't take long to find that Cross Questions and Crooked Answers is a game that he is referencing. In the game, a group of people formulate questions which they answer normally, then they mix things up so that each answer goes to a different question. For instance, one question might be "What's your favorite food?" to which the answer given is "Pizza." Then another question might be "What could you find under your bed?" and the answer given is "A giant dust bunny." Then, after mixing the questions and answers, you could get "What's your favorite food? A giant dust bunny."

[@odileelido8407]

A bit like this? kzbin.info/www/bejne/h4PLqpZra8aJmJI

[@bernhardwerner8095]

John's definitely in the house. Don't let anybody tell you otherwise.

[@EdithKFrost]

The problem of the last one is that you know John is in the house, but you don’t know if John is in the house having a toothache

[@George4943]

They never mentioned a piece of text on page 22. "Now in representing the two premisses, I prefer to begin with the negative one ... because the grey counters can be placed with certainty ...." This seems sorta key to how CD intended his playing board to work.

[@GrahamDawson]

“There is no one in the house but John” would presumably be better (less ambiguously) rephrased as “There CAN BE no one in the house but John”.

[@SgtSupaman]

This is definitely a better phrasing for what was intended.

[@Morzalius]

Was about to comment the same thing. "There is no one in the house but John", at least in my eyes, most intuitively answers the question "Who IS in the house?", rather than "Who COULD BE in the house?". That "is", at least in modern day, implies certainty.

[@trejkaz]

I personally prefer the reasoning that “There is no one in the house but John” rules out non-Johns from being in the house, but doesn't tell me anything about whether John-with-toothache is in the house, nor whether John-without-toothache is in the house. Usually if I were doing some kind of logic puzzle, I would draw a single oval covering both squares, to indicate that there is exactly one true inside that loop, but that we don't know which cell it's in. Come to think of it, knowing that John _is_ inside the house should mean that you can rule out John being out of the house as well. But the solution didn't put 0s in those locations either. So yeah, I dunno what they (the problem-creator) were thinking.

[@Mika_Storm]

Deducing the rules by: 1) coming up with a hypothesis 2) doing an experiment 3) comparing the results with reality (the solution) 4) refining your hypothesis 5) repeat is kind of a game of scientific experiments that you added for yourself 💚

[@Mika_Storm]

Since I sometimes don't get the maths in your videos, it made me really happy to have caught on to this one early and getting most of the games correct by myself without pausing 🎉

[@TheZotmeister]

Aaaand this is why I've been campaigning that logic needs to be taught as its own course in grade school.

[@retoc3595]

i laughed so hard at this video😂😂😭. Nice vid guys!

[@benkielstra5910]

It’s cool to see the struggle to recognized definitively true and definitively false. Based on the language there is definitely a John in the house, but we can’t say he does or does not have a toothache. therefore neither is definitively true. It’s like a sudoku where you know two numbers must be in two squares (very helpful in eliminating possibilities from other squares) but you don’t know which square either of the aforementioned two number goes in. Love this game!

[@Ruddigore]

Question 8 had me screaming at the monitor - Why have you put those two blue counters down.... A super video, loved it.

[@rgoodwinau]

Very entertaining (to watch) !!!

[@michaelwoodhams7866]

Here is a Dodgson/Carroll puzzle I am fond of: A man holds a very small dinner party, of himself, his father's brother-in-law, his father-in-law's brother, his brother-in-law's father and his brother's father-in-law. (As I recall, this is as much as Dodgson wrote. The puzzle is implicit.) What is the smallest this party could be? Draw a family tree. (To follow the law of the UK, first cousin marriages are allowed, but nothing closer.) Bonus points (this is from me, not Dodgson): what is the least relaxation of marriage laws which would allow you to reduce this number?

[@TheRealD4]

Can't believe I'm trying to answer this but I believe it is 3 people in total? His father's brother in law would be his aunt's husband who could also be his father in laws brother, i.e. his wife's uncle. His wife wouldn't be related by blood to him whatsoever. So these two are the same person. However if his brother in law's father was also this same person then it would mean his wife's father was married to his auntie so they'd be first cousins which is forbidden. But this person could still be the same as his brothers father in law IF his brother married the sister of his wife. So altogether we only need 2 extra persons making 3 in total. And to answer your bonus question, I would guess that relaxing the law on first cousins would mean all 4 could be reduced to the same person (lol?) making just two people in total at the dinner party?? Go on what's the answer then? 😂😂

[@michaelwoodhams7866]

@@TheRealD4 First cousins marriages *are* allowed, just nothing closer. Spoilers ahead for anyone trying to solve the problem . . There are two people: the host and one other, who fits all four roles. I don't remember the solution off the top of my head. Remember that 'brother-in-law' can either be sister's husband or wife's brother. With uncle/niece and aunt/nephew marriages, he can dine alone, and is probably a Hapsburg.

[@jmich7]

Me louve James Grime, long time no see or hear!!! + HISTORICAL Thanks!

[@gcewing]

I'm getting flashbacks of Karnaugh maps from this.

[@johngamble5270]

Substitute "flashbacks" with "fond memories" and yes, K-maps were the first things I thought of. (I really liked my digital logic course.)

[@AndreaDragotta]

A similar logic and sentences-based game is called "logic grids", if you want to do a similar thing, but have a way nicer experience 😊 (it's not a specific app but a type of game)

[@KaliFissure]

@tomrocksmaths I just discovered your channel. Thoughts on this form? It suggests renormalization via rotation on z axis. Surface(cos(u/2)cos(v/2),cos(u/2)sin(v/2),sin(u)/2),u,0,2pi,v,0,4pi

[@tomkerruish2982]

Would it help if you guys used quantifiers and predicates?

[@drmcallis]

The book is available both on the Internet Archive (as noted above) and on Project Gutenberg, if anyone is looking for a copy...

[@gerrytoft204]

A quick Wikipedia search tells me that Venn diagrams were popularised in the 1880's. So this game is before Venn diagrams. Or at least before Venn diagrams were in wide usage.

[@TotemStorms]

"I am not aware of any game that can be played with less than this number." I've come to this video via one of Sanjeev Bhaskar reading one of Spike Milligan's letters home ("I am officially, Somewhere Else. That Somewhere Else is where I am. I am not at liberty to say."). Apparently that's the direction that the world wants me to go today...

[@johnedmundson5196]

I'm pretty sure the version in the anthology had an appendix that compared to the newly published (never going to catch on) equivalent method of professor Venn.

[@johnedmundson5196]

Its in the "symbolic logic" version appendix note 5. In note 6, he does exactly what tom and Bradley does in reverse.

[@pieterp2329]

I think I understand why John is in the house but does not have the tokens placed. Let's say there is just one John, he can't be two tokens, one with a toothache and one without a toothache. So John is in the house but you do not know if he is in the toothache-room or in the non-toothache-room so you cannot place both tokens.

[@thejackscraft3472]

entirely possible, though there is some evidence to cast doubt on that being the reasoning, since if John was definitely in the house the section at the top right (John not in the house) should have had a 0, as it would be impossible.

[@trejkaz]

I did the same puzzles by just writing out all combinations on paper and crossing them out as they were eliminated, and hit all the same problems with the wording of the problems. LOL Also I wanna say if you draw the Venn diagram circles a little more rectangularly, and overlap them in a particular way... that you'd end up with that square diagram anyway. 🤔 Is there some kind of computer-based logic system where you could feed the same statements in, have it do the inference, and get the right answer?

[@gamingtekkerzz7026]

I think the biggest problem they came across was assuming that because something was possible it was certain (i.e. it they thought it should be =1 whereas it should be ambiguous). John was in the house, but we could not determine whether he did or did not have a toothache. Therefore, we cannot assume either are true as we don't know which one is (one must be, both could be, but we have no proof of which) so we should leave the region blank.

[@justinjustin7224]

I drew up the board for myself and played along with the video, and I'm glad to say that I got everything correct aside from the last one. Though, I did have an unintended advantage in that I paused to read the pages shown in the video aside from the answer pages, lol.

[@justinjustin7224]

I even did the question they skipped that requires choosing a universe and coordinates, setting them as: universe="what he could bring me" m="I wanted it" x="a kitten" y="a kettle" Interestingly enough, my results confirmed that we don't know whether I was brought a kitten by him or not, just that he definitely brought back a kettle that was _not a kitten_ (otherwise it wouldn't have been a mistake).

[@gamegotten6637]

So consider giving me some Mathematical Tips Btw I do have read Lewis Caroll's Alice In Wonderland and Through the Looking Glass Loved it!! I think you are a chivalrous and cheerful dude Sorry you are a doctorate So i must call you ---- a doctor ❤❤ Splendid!!

[@gary.h.turner]

Some dudes are chivalrous and cheerful. No doctors are dudes. Therefore...?

[@RoderickEtheria]

If some red apples are unwholesome, but no ripe apples are unwholesome, then some red apples are unripe. All dragons are uncanny. All Scotchmen are canny. No dragons are Scotchmen. No old rabbits are greedy. All black rabbits are greedy. No old rabbits are black. All well-fed birds sing loudly. No birds that sing loudly are unhappy. All well-fed birds are happy. John is in the house. Everybody in the house has a toothache. John has a toothache. I have been for a walk. I feel much better. This doesn't mean that if you have been for a walk that you feel much better. There is no one in the house but John. Nobody out of the house has a toothache. You can be outside the house without a toothache, but John may or may not have a toothache but is in the house.

[@gamegotten6637]

Hello Tom; I am from India Have always been, a great supporter of your channel I love maths too Currently I'm in class 9 In India,basically the maths syllabus is not huge but a little bit lengthy But I'm good in calculations The only reason for writing this comment is because, No Matter what others say, keep your content .Be an Edu-KZbinr.You have my support.❤❤ Love it!!

[@IntelVoid]

Late to the party and probably beating a dead horse, but: It's not that John isn't necessarily in the house. It's that John can't be both in the house with a toothache and in the house without a toothache, but both of those segments had a blue counter. As mentioned earlier, blue counters mean 'definite', not 'possible'. So be careful where you put them. Only place blue in a segment if you know all THREE conditions for that segment are met. (If I were playing I might put one on a border if I knew 2 conditions but not the 3rd - rather than in both as kept happening here)

[@hadz8671]

I have this book as a Dover reprint.

[@gcewing]

I wish this house existed. I would just have to avoid going there and I would never have a toothache.

[@shanetomlinson561]

I think you just don't know whether or not John has a toothache. You know he's somewhere in the house, just not sure on the toothache status. I like this game and the collaboration

[@benjaminabbottscott]

I certainly hope he meant "dragoons"

[@vrixphillips]

this might be my new favorite board game lol

[@Censeo]

"All dragons are uncanny". My immediate thought was, this could be a true statement even if all dragons don't exist, but then I realized I was over thinking it because existence wasn't relevant to the logic.

[@mosesgklein]

In modern semantics, "all A are B" is true if there are no A. But in Aristotelian logic, which is the basis for this game, "all A are B" implies "some A are B" -- Aristotle seemed implicitly to understand that we aren't going to talk about categories that don't have at least one instance. That wouldn't work for Fregean predicate logic, because when you allow compound terms, you may have a conjunction that has no instances -- but if you restrict your attention to syllogisms, as Aristotle did, it's a plausible semantics, even if it does seem wrong to students of logic post-Frege.

[@OneTrueBadShoe]

On the last one, i literally screamed, "John is not 2 people" several times. Since there is only one John, you can't put a 1 in multiple boxes. If you don't know where he is it's left blank. I think it might be the Venn diagram causing confusion. Placing markers where things are possible is not intended. Placing markers is only for impossible and certain. A box with no marker means it's possible but not certain.

[@andrewholdaway813]

Ahh a game created before scotchmen became scotsmen for reasons unknown, but probably victorian whiskey distillers.

[@fdagpigj]

Man, this was painful to watch, but maybe that's to be expected from watching old men playing a teenager's game ;) Btw, even if the wording implies that John is in the house, it says nothing of him having a toothache, so you would not know which quadrant to put him in. Having both as blue means there's at least two Johns, one of which has a toothache and another who doesn't.

[@drziggyabdelmalak1439]

True.

[@thejackscraft3472]

That then would rule out John not being in the house, so that section would have had a 0, which it didn't. so while that could be true, there's enough evidence that it's not what was intended to cast some doubt on that being the reasoning.

[@fdagpigj]

@@thejackscraft3472 I don't follow. Are you claiming that my argument is that there cannot be two Johns? Because it isn't. It's just that it's nowhere declared that John has a toothache or John doesn't have a toothache. So you don't know either to be true for sure, which means you cannot put a 1 on either slot, because it is possible for (both or) only one of those cases to be true and you do not know which.

[@thejackscraft3472]

@@fdagpigj The statement "There is no one in the house but John", is a statement about a singular "John", as is labeling the X axis "John", it's not "Johns" plural, as it is with the rabbits. So yes, it's a singular John, so he cannot be both inside and outside the house at the same time, thus there is a mistake in either the question or the answer.

[@benjaminlehman3221]

a grid with checks and X would be better than a venn diagram

[@EastBurningRed]

conway’s game of life doesn’t require any players, though carrol couldn’t possibly have known about it

[@Marguerite-Rouge]

Personally, I understood the sentence "nobody is in the house but John" as: "John is actually in the house, but if he is in the house, he can't be outside"! So I will put one blue token in m and x but between y and y' (because we don't know whether John has a toothache or not) and two green tokens in (m' and x and y) and in (m' and x and y').

[@PiAlphaUpsilonLambda]

the basis of the game that if we dont know if its y or y', we dont know which box, and therefore cant make any conclusions. Even if we know John is in the house, we dont have enough information to put a token in a particular box, hence they are left blank. But i agree with you there should have been a green token in (John, outside, no toothache) because we know John is inside the house (but dont know his toothache state).

[@PiAlphaUpsilonLambda]

revision to my earlier reply: i noticed that in some of the other answers in the book not covered in the video, they show a number 1 sitting on the line between boxes, so perhaps a john with and without toothache should also be shown as a token between the two boxes. But then perhaps that is more questions where there are multiple things being spread out (i.e., 'some' rabbits are ..) whereas because there's only 1 john???

[@Marguerite-Rouge]

@@PiAlphaUpsilonLambda It's a linguistic issue actually! Personally, I think we consider only one John, otherwise the sentence should be "Nobody is in the house but Johns" or "people named John". And yes, I saw these ones on lines between two boxes so I assumed they are used for these ambiguous cases.

[@dalriada]

It’s baffling to me why these accomplished mathematicians had so much difficulty with this. Especially once they hit on using Venn diagrams. Are these separate skills?

[@PiAlphaUpsilonLambda]

No old rabbits are greedy does not mean all old rabbits are not greedy. there may be no old rabbits.

[@raylightbown4968]

I was taught syllogistic logic in 1966. So, I followed Charles quite well. Your problem is that he doesn't explain that words like "all", "some" and "no" have inclusive and exlusive meanings. So do "and", "or" and "but". For example, "or" can mean "both". It isn't the same as "either or" As you conclude it is a language problem because he isn't explaining the meanings (his meanings, Aristotle's meanings) of the relevant words.

[@thelordz33]

I don’t get why the second one was so difficult. If all dragons are uncanny and all Scotchmen are canny, then no dragons are Scotchmen and no Scotchmen are dragons.

[@andrewholdaway813]

Because they couldn't get past their fake confusion over scotchmen

[@ParadoxProblems]

I think the game intends "No X are M" to leave the existence of "X that are not M" undetermined while forcing the non-existence of any "X that are M". Similarly "Some Z are M" leaves the existence of "Z that are not M" undetermined while forcing the existence of "Z that are M" "All Y are M" seems to imply the existence of some "Y that are M" and the non existence of any "Y that are not M" Explicitly, the functions of the game determine the following All(X,M) → X=M & Not(X=Not(M)) Some(X,M) → X=M No(X,M) → Not(X=M)

[@quesoestbonne]

Karnaugh maps?

[@hihibybyby7217]

can u solve Korea uni entrance exam math its another level from any other countries

[@oriosi]

As a John, watching this inside a house, I am upset that you have given me a toothache.

[@ChymistTycho]

Don't worry John, they also gave you not a toothache at the same time.

[@iuriikononenko9238]

Considering 3 possible outcomes (definite, possible, impossible), there should be tokens of 3 colours.

[@PiAlphaUpsilonLambda]

the real point of the game is not merely to get the token places correct, but, having placed the tokens, be able to make some new statement about the 'universe' - hence be able to conclude from the diagram that no dragons are scotchmen (and vice versa), or all well-fed birds are happy. hence the propositions at the start of the book.

[@davidallen6009]

No tokens = possible, so 2 colors is fine. Just wish they had used the colored tokens as intended.

[@MrClarence1126]

I think the blue/green are. for positive/negative assertions. I don't know why they "take one. away". They took away the intersection of black and greedy, which was wrong.

[@alanmon2690]

"Scotchman", historically, for hundreds of years Scotch was the correct term for someone born in Scotland. Then in about 2005 someone reaiised that this also referred to a dangerous, poisonous, addictive liquid that killed hundreds and then they became Scots.

[@dalriada]

More like 1985.

[@alanmon2690]

@@dalriada it was about 2005 that a Scotchman from the Orkney said on a message board that he now preferred Scotsman because Scotch was a drink and he did not want to be associated with it...

[@MrJaffjunior]

In moment 27:46, "No old rabbits are greedy", there was a mistake. The statement doesn't mean you can place a blue chip on the upper left of the venn diagram. It only means that you must put zeros at the intersection of old and greedy. This might explain why, at 31:40 your diagram did not match the answer.

[@Firebird1005]

Please do a follow-up to tell us why the last answer was wrong. Loved the deduction process you went through to get to the rules.

[@scragar]

The last one is just badly worded. It said "there is no one in the house but John." A better way to phrase it might be "Everyone who's name is not John is outside the house." It wasn't trying to imply John was in the house(which is why it should be blank, we don't know if John is in the house or not, only that everyone else is outside).

[@Firebird1005]

@scragar rephrasing the question is not a valid option. Investigation in linguistics change over the years is. The follow-up with a linguist with knowledge of contemporary uses of language would be something I would like to watch.

[@fussyboy2000]

All that without writing a single piece of symbolic logic. Proably for the best all round though.

[@EdithKFrost]

No x are m just means x intersect m is empty. But is there an x at all? We don’t really know if x intersect not m is empty or not, so that’s why the author didn’t put a 1 in that corner

[@FelixNielsen]

There is no one in the house but John. (Not one OR John, i think but it is fishy) Only John may occupy the house Nobody, out of the house, has a toothache. Only John may have a toothache. If John do have a toothache he must be in the house. If John do not have a toothache, he may be in or out of the house. Poor john.

[@acorn8773]

No old rabbits ar greedy means there are no greedy old rabbits, but that doesnt imply that there even is atleast one old rabbit so we dont know if there are non greedy old rabbits (because we dont know if there are old rabbits at all)

[@gurjotdosanjh7828]

For that last one, I think John is in the house for sure, but we don’t know whether John has a toothache or not. And if we aren’t sure about something, we just leave it blank, so that’s why it’s blank.

[@justinjustin7224]

If we know John is in the house, then it logically follows that John must not be in the house. That is unless "John" is the collective of all people named John, and not a single individual. Though, probably more relevant is the fact that the game only has 4 tokens to represent what is surely false, and there being only a single John who is for sure in the house would introduce the need for a 5th false token. Also, I paused to read the pages shown in the video, and there is mention that it is the "usual rule" to place a single red token on the boundary between 2 statements that can be true, but are not differentiated yet (on page 23, as can be seen at 10:29). And looking at the archived version of the book linked in the description, it is shown to be represented with a "-" through the boundary, so they seem to actually be claiming that we can't say that John is in the house. Edit: read the amount of tokens required again, and there are supposed to be 5 grey tokens ("counters" in the book's words), so Tom and James actually had swapped which color was supposed to be which; I also just have to assume that "John" does, in fact, refer to anybody named John, and that we cannot conclude that one of them is in the house. No clue if that's just a drifting of the interpretation of language, or perhaps it truly is an error on the part of the author.

[@drziggyabdelmalak1439]

YES! That's it. I've been trying to work it out. Cheers! Hope the two Maths profs read this!

[@LieuweStraatman]

Why? Why is it that matter at the edges of the universe appears to move faster then it should (according to modern theory). The simple solution is that there is non visible matter present holding the universe closer together then previously thought. This dark matter would act as a solidifier tying the ends to the middle making it having to keep up even though it has to travel longer distances to do so, simmilar to those death machines in playgrounds where you can go to the middle turntable and then proceed to step to the outer edge to enhance the risk of early neck trauma. Let's try and find some other ways into this phenomenon. The first argument I'll be presenting is a relativistic one. We know there are two ways to slow down time, one is to have a lot of mass, the other is to go really fast. If we want the entire universe to have undergone the same amount of entropy we need some way to compensate for the lack of mass. In order to stay within the same timeframe (implicit positive correlation between entropy and time) the matter at the edges of galaxies has to be moving faster. The second argument I'll be making has to do with the difference between rationality and irrationality. If we want to condense matters doing this rationally is probably your best bet, pretty much the reason why your mom is better at packing than you are. This translates to the positive correlation between matter density and rationality. In other words, matter at the edges of galaxies tends more towards irrationality. For a quick sidenote: the symmetry breaking (irrational) weak force doesn't act on light (strictly), this might clarify why this irrational matter is mostly invisible. Rationality is indifferent to direction, it doesn't really matter how you lay a football for a free kick. This is unless you believe in hitting the ball at the valve for that infamous knuckle effect, which is exactly keeping the irrationality behind the primary interaction surface, letting it act indifferent. But this is all a little to deep, so let's resurface. In principle an irrational object is a lot more unidirectional. Throwing an American football, orientation matters. The irrational shape of the American football allows it to cut the air better, allowing for greater throwing distances. Irrationality allowing for advantages doesn't break the principle of entropy, since any small advantage you gain in one orientation greatly increases the disadvantage of any other orientation. In short: reality is slowed down in two ways, mass and speed. The more rational condensed centers of galaxies are on the side of using mass while the irrational edges are more on the side of using speed. In this way there is at least an inclination towards less entropy.

[@TroyLaurin]

This appears to be a game teaching logic maps. I think you would have had a much easier time if you used both tokens on a single board - one colour to specify predicate combinations that you know to definitely be true, and the other colour to specify predicate combinations that you know to definitely be untrue or impossible. That's what the book was referring to with 0 and 1 in its answers. Edit- you realised this yourself at 25 minutes, but you chose hard mode. I wonder what Lewis Carroll would have made of modern zero player games?

[@Harrykesh630]

two NUMBERPHILES together

[@acorn8773]

51:40 john may have a tooth-ache, he may not, we don't know your solution has him both having and notnhaving it

[@closerhawk687]

Do an ib exam

[@jaydee5022]

Could you please draw the Venn diagram to show Victoria Atkins and Rishi Sunak the total lack of logic when I can't get an appointment at St George's hospitaĺ 6 weeks before the follow-up appointment with the consultant to check (6 weeks after said injection) to see if it is working. The 3rd circle being the obligation posed by the Hippocratic Oath which implies that the medics should be striving for excellence and best possible care of their patients. I was told that "at least I would see the doctor" - a waste of both the consultant's and my time (& my boss's) which won't result in pain relief or a diagnosis and thus means I have to wait another 6 months for a second follow-up appointment just as the injection wears off. I think if they could see this expressed in either your game or a Venn diagram the twisted illogicality might just become apparent.

[@asheep7797]

4:22 A comedian, but an incorrect comedian. The Game Of Life.

[@KaliFissure]

Labels. Help. Clarity. 🙂🖖

[@ricomariani]

It looks like Karnaugh maps to me, only they haven't done the usual permutation of 0/1 to make it so that you can draw loops around the groups. :D Karnaugh maps can represent much bigger logic sets than venn diagrams economically. en.wikipedia.org/wiki/Karnaugh_map

[@lilpunkxd722]

The last one from a logical point of view doesn't say anything about John. "But Jhon... what?"(could be anything) You know what I mean? It doesn't say. The whole game is a language thing. Besides the getting rules you also have to stablish what terms like "some", "if... Then", "not all" means on this particular context(wich makes u play against your own intuition).

[@djwilliams8]

Feel "no one in the house but john" statement means you cant have john in the house as it would contradict first statement that no one is in the house.

[@SgtSupaman]

The entire thing is a single statement. You can't just say "no one is in the house" is a statement, because "but John" cannot be a stand-alone statement.

[@stiofanmacamhalghaidhau765]

what it says is essentially 'we don't know if there is anyone in the house, but if there is, it'll be john on his own.'

[@phiefer3]

34:00 the book isn't wrong. You've once again assumed a non-empty set when the first proposition only mentioned empty sets. You've assumed that there are old rabbits, when the first statement did not confirm that. I believe, as you mentioned earlier that the 2 colors are supposed to represent 1s and 0s. So when the first statement says "no old rabbits are greedy", you should not be placing 1s in any part of the old rabbit circle, instead you should place a 0s in the old-greedy and old-greedy-black regions. Then the statement "all black rabbits are greedy" tells us that there is a 1 in the black-greedy region, and also that there is a 0 in the black-old and (just)black regions. Which matches the book's solution. On the last one, I think there is a bit of a language thing, but also an overlooked detail. Even if you assume that "there is nobody in the house except John", to mean that John is in the house, we cannot put a 1 in the "john-in house-toothache" or the "john-in house-no toothache" regions because we don't know whether or not he has a toothache. We can't assume that John has a toothache nor can we assume that he doesn't, therefore they're both unknown. I personally, also had a 0 in the John-outside-no toothache region because I also assumed that the first statement confirmed that John could not be outside the house, which is where I think the language issue comes up. I don't know if this question is meant to only refer to a specific John, or "all Johns", if the latter then maybe the first statement should have been that there are no non-Johns inside the house, leaving it unknown whether or not there are any Johns outside (or inside) the house.

[@benjaminlehman3221]

1:22 no gloves?

[@Firebird1005]

Gloves make your hands less sensitive and catch easily on the edge of a page, thus damaging the page. Contrary to common belief just washing your hands makes them save to touch the book.

[@Ashbakhaaz]

omfg please read the book... you struggle because you didn't read! :')

[@psiphiorg]

With the problem of the rabbits (with old, black, and greedy as the properties), I think the reason your answer didn't match the books' answer is that you assumed that some old rabbits exist. The problem doesn't say that; it merely says that no old rabbits are greedy. So you are assuming that some old ungreedy rabbits exist, but maybe they do and maybe they don't. The book leaves that blank because it doesn't make that assumption.

[@Mr_AbdulRehman]

Sheldon??

[@eosrose6126]

Two colors are maybe representing positive or negative statements. e.g.. blue is positive and green is negative? R (Om), R(By), R(Gx) 1. R(Om) ≠ R(Gx), 2. R(by)=R(Gx) 3. R(by)≠R(om) That means 1. Old rabbits are neiter black nor greedy 2. All black rabbits are greedy 3. No black rabbit is old So in a rabbit universe the statement old can only be on m- axis and on the negative side on the x axis So a green playstone must be placed on m axis into the left x quadrant. For attfibute greedy a blue stone is placed in x,y quadrant. only two stones are necessary. If this is wrong , i don t care, it was a lot of fun....omg is this a math pun 😂, i m not a mathmatician, so i just tried it my way 😊

[@drziggyabdelmalak1439]

Ouch! Victorian teenagers must have been weird if they understood that! Or brilliant! Er, the last one is very confusing. Surely, however you 'read' the language John IS in the house? Also the question says nothing about John and toothache! I'm lost!

[@stiofanmacamhalghaidhau765]

what it says is essentially 'we don't know if there is anyone in the house, but if there is, it'll be john on his own.' so, 'there is' needs to be read as 'there can be' in modern phrasing. and yes it is almost certainly deliberately obtuse. the goal is to force a very particular approach to analytics. you can infer nothing. you can only speak to the information given. the information given can be positive or negative, and neither implies a converse exists or that any of the things referred to exist. taking a different puzzle, we could infer from 'no old rabbits are greedy' that old rabbits exist but that's not what we're told. all we know is that rabbits that are both old and greedy do not exist. no greedy rabbits may exist, old or not. no old rabbits may exist. all we know is that if an old rabbit exists, it will not be a greedy rabbit. total mindfuckery.

[@BooleanDisorder]

Squeeeeeee! 😊

[@tobiasactually]

Probably the most exciting, boring video ever. Thanks, guys.

[@petermcandrew7787]

"Some ..." is equivalent to ∃ "there exists". And "No ..." is ∄ "there doesn't exist". You kept falling into the trap of standard English implication, where saying (for example) "some red apples are unwholesome" would imply that there are also red apples which are wholesome. The statement, however, is meant to say "there exists at least one red apple which is unwholesome".

[@DataRae-AIEngineer]

Hello from across the ocean where we call it "math". You guys sure have fun over there. Our library doesn't even allow us to touch the books anymore lol. They're all just scanned copies. Anyway, it's an instant subscribe from me.

[@retrogiftsuk4812]

In case you don't notice, there is a link to the PDF of the book in the video description... ALSO... When they were being confused by the book's explanation refering to "box 5" that is because as well as the book containing a board to play on, there was another copy in the book and that one had numbered squares (to help with the explanations). The numbered squares version is on page 10 of the PDF.

[@rowandee3470]

I thought these guys were the same dude

[@gmeast]

Why isn't she wearing gloves?

[@lilpunkxd722]

The book start quite until we get to the rules of the game when it became a nightmare. (⁠ノ⁠｀⁠Д⁠´⁠)⁠ノ⁠彡⁠┻⁠━⁠┻

[@manticore5733]

As a UK collector of Lewis Carroll (especially books) and a lover of maths and puzzles this video is just my thing... annoyingly I never bought this book as I tend to hold out for first editions at unrealistically low prices. Typing as I watch your video. "Some" is equivalent to "There exists"... humans are animals (this includes Scotchmen!)... Greedy old black rabbits... you're definitely falling foul of trying to apply the logic as you're placing counters rather than blindly placing counters and looking at the result: I think what you needed to do was decide one colour means "FALSE" and one means "TRUE" and place the appropriate ones that fit the statement - in the end you'll have some contradictions (both colours in a box), some positive, some negative and some unknown -> that'd give you a very clear view of what is impossible to exist and what is unknown as well as the "all are" and "none are" conclusions. (Ah, just got to you reading the answer... yes he seemed to be missing a 1 in the xym inner top left box, but it made a contradiction then in logic terms you AND the content of a box: 1 AND 0 = 0... hence he correctly had 0 in that box) So if you placed 0 and 1 counters the first statement [No x are m] means place an 0 in xym and xy'm ; then the second statement [All y are m] means place a 1 in xym and x'ym and an 0 in xy'm and x'y'm ( total of 6 counters placed) - as the y side is full of counters with only x'ym having a 1 (note: xym has 1&0 => 0 making the diagram in the book) the new statement you can derive is [All black rabbits are young]. You can also say [No old rabbits are black] but nothing stronger because you don't know anything about old non-greedy black rabbits (xy'm') for example. Singing birds - you just forgot the negatives of "ALL" ... ah I see you worked that out. Toothache - I think you had it right this time, anybody in the house who is not John will have toothache... xy'm being true doesn't say there is another person in the house: it's like saying "All the notes in my wallet are £50 notes" - the statement is true when I have no notes in my wallet. ...but John - definite language issue there, if it was written "No-one else is in the house" or even better "Only John can be in the house" then it'd be clearer. ------------------------------------------------- Great video you guys, it's so real and comforting to see well educated people stumbling through things like this - had to laugh at the "maybe we should have read the manual" moments, so very true to everyone rushing into a game. If you liked being baffled by Dodgeson's wordy language you have to look through his book "A Tangled Tale" - a collection of narrative maths puzzles he'd first published in a periodical; the answers include his replies to correspondents who tackled them originally. They are great examples of pulling the maths out of a situation and recognising what is and isn't relative as well as being good maths problems in there own right. ...and that book I do have a first edition of. ;) --------------------------- Fun fact: after the first Alice book the royal household requested a copy of his next book... and were quite surprised to receive a book on Symbolic logic!

[@TimeSprout]

This is unbearable. Like watching an elderly relative play video games.

[@MrBradleykeith]

Boolean logic

[@SergioJuantwn]

Hey , can i see your tatoos i love them , pleeasseeee

[@Nefariousbig]

I can't be the only one who thinks arguing over what he game even is when learning it is part of an intended meta game happening at the same time... The description seems deliberately obtuse and full of moments of befuddlenent, especially for an author who you would assume would be very capable of a more refined tutorial. Awesome to behold!

[@tolkienfan1972]

I'm sorry, but you are both terrible at this. 🤣

[@gejyspa]

*sigh* If this is the current state of British Maths education,, I'm not sending my grandkids to Oxford