Reply to Banno I didn’t realize I was creating an inconsistency, so I leave it up to another poster (first comer) to decide to reject either my axiom or John’s.
But can there be an integer bigger than another integer?
What does bigger look like here?
Harry HinduDecember 25, 2019 at 03:09#3658870 likes
Reply to Banno Well, what do you do so you can give half of the fruits of your labor to me?
Math games with arbitrary rules are a useful waste of time. If you really want rules, reality has some for you. For math or language to really be of any use, they need to inform and predict the world as it was, is and will be.
Harry HinduDecember 25, 2019 at 03:27#3658910 likes
Reply to Banno "Rules" is probably the wrong term to use. Any mathematics without real-world applications would be the game you're looking for. Knowing how many miles to the next rest stop and how fast you are going isn't a game when you really need to empty your bladder. It produces true knowledge about you and the world. Is your game useful for anything outside of this thread?
Let's say the rules of arithmetic are arbitrarily made up, like Banno's math game. The golden ratio is one result of arithmetic. The surprising thing is that it can be find in spiral patterns in nature. Now why might that be? Perhaps the rules or arithmetic are not so arbitrary.
Let's go back to their origins. How did humans come up with arithmetic? Probably when it became useful to track transactions and taxation. And that's not arbitrary.
The contention here is that this game has similarities to mathematics, in that the playful creation of rules is at the core of both.
So let's try this out. I as ruler of the nearby city demand you pay a tax. I have my soldiers take three oxen out of your six. You complain that this only leaves three oxen to plow the fields. My official reply is that six minus three is five, by decree. I have only removed one of your oxen.
For some reason, that system doesn't last and is replaced by the 6 - 3 = 3 one we have today.
Right, so is math about useful patterns, or about making up arbitrary games, like Chess and Go are made-up games with well defined rules that allow for interesting patterns?
he patterns are forms, they are not useful, they are expressions in the extension of matter and energy.
The forms are dynamic, and they have dependence of ....time.
I don't mind your inconsistency. It is like the food I cook for my children... it has a certain uncertain flavour peppered with a consistency of indescribable inconsistency.
Let's go back to their origins. How did humans come up with arithmetic? Probably when it became useful to track transactions and taxation. And that's not arbitrary.
Thats why I proposed the rule that Banno hand over 50% of his dough. I thought we should start where the ancients did when the rules were meant to be applicable in the world.
Harry HinduDecember 25, 2019 at 17:00#3660530 likes
How is 3+3=6 useful for knowing how much of my income the government wants? If the government wants 50% of my income, do I just write 50% on a sheet of paper and then give it to the government? Are we just writing scribbles with arbitrary rules? If so, then why isn't the government content with a sheet of paper with the scribbles 50% on it? What is 50% OF something? What does the "of" mean?
Reply to Moliere It's the 'many worlds' interpretation of mathematics.
Always "and", and never "or", but also "or"... Etc.
Banno's thesis is that maths is invented, not discovered, just as games like chess are. Well then it is very easy to invent some rules for a game or some rules for a mathematics, and there are lots of them. But most are dull or unplayable.
So the thread itself is badly set up as a game that doesn't have much interest or significance, because posters can, and nearly always do, take the nuclear option and pretend they have "won". A better win might be if we could come up with a new form that was consistent and incomplete, but not isomorphic with arithmetic or something like that. I don't have a better set up that would encourage that, unfortunately.
A better win might be if we could come up with a new form that was consistent and incomplete, but not isomorphic with arithmetic or something like that. I don't have a better set up that would encourage that, unfortunately.
Me either.
Though I think your insight here is worth preserving:
So the thread itself is badly set up as a game that doesn't have much interest or significance, because posters can, and nearly always do, take the nuclear option and pretend they have "won"
The nuclear option -- contradiction -- is something like the fruit on the tree in paradise?
Banno's thesis is that maths is invented, not discovered, just as games like chess are. Well then it is very easy to invent some rules for a game or some rules for a mathematics, and there are lots of them. But most are dull or unplayable.
This, though, is the stronger point.
If the King is in check then the other player can swipe away the peices, but this is rude (and so it goes with the other games; the dull and unplayable games seem to proliferate, and the interesting ones are the ones we ought go for)
I think math is probably like chess, but that chess was built upon mathematics: so the metaphor is good, but starts on the wrong side.
If the King is in check then the other player can swipe away the peices,
That might be (but actually isn't) an interesting game, but it is no longer chess. Allegedly, rugby was invented when some idiot was supposedly playing football and picked the ball up and ran with it. A few other things had to change before it became a game worth playing.
There is a card game called "52 card pick up", in which the dealer throws all the cards up in the air, and leaves their opponent to pick them up. It's faintly amusing. Once.
As does 52 card pick up. But if you want to do something interesting in mathematics, or the philosophy of mathematics, this is not the way to go about it.
That might be (but actually isn't) an interesting game, but it is no longer chess. Allegedly, rugby was invented when some idiot was supposedly playing football and picked the ball up and ran with it. A few other things had to change before it became a game worth playing.
There is a card game called "52 card pick up", in which the dealer throws all the cards up in the air, and leaves their opponent to pick them up. It's faintly amusing. Once.
I'll admit that that's not my favorite game. And there are only so many times I can play it.
Though what becomes shit was at one point food Reply to Banno
What of us who think it is both created and discovered? — jgill
Sounds contradictory to me, unless you are saying the application of it is discovered
It is a bit fuzzy. But here is an example: Linear fractional transformations have been around for years but at some point someone discovered they could be categorized by the behavior of their fixed points. One such categorization was "parabolic", in which the fixed point demonstrates both attracting and repelling behaviors. Thus, a category was both discovered and created. When I determined the conditions under which infinite compositions of parabolic transformations converge to their fixed points years ago that was a discovery based upon a creation.
And speaking of which, category theory could be considered a creation, then its characteristics follow as discoveries.
However, I am open to other perspectives. Most mathematicians don't care to argue the point. But it is certainly fair game for the philosophically inclined.
Reply to Deleted user You're taking the game too seriously. But it is the attitude I've seen most people take in posts discussing logic, riddles, games, etc. When they interact with me I feel hugely overwhelmed.
They believe I am trolling, but I simply lack wording and reasoning.
New rule: The sum of the product of any two integers is omega minus (now corrected!) the double of Lionino’s integers.
Reply to Mikie Because you asked so nicely and I can't help myself, I'll chime in briefly on the topic of whether mathematics is created or discovered:
I think that the distinction between creation and discovery only applies to concrete things, and for abstract things like mathematics there is no such distinction. Because there we're dealing entirely with matters of possibility, so to discover something is just to show that it is possible, as in, it could be created, at any time; and conversely, to create something is only to show, and so discover, that it is possible, and always has been.
It's only with concrete things that exist within time that they could have already been actualized (in the past) and so be available to be discovered, in a way distinct from not having been actualized yet and so being available to create (in the future).
Deleted UserAugust 08, 2024 at 00:50#9236650 likes
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But under my definition we will have uncountably many subspaces of R2 that are not subspaces of R1, for example.
I think I can see it. By uncountable in your definition, it means that there are infinite subspaces or dimensions. Right? It is not about to be countable but if the vector space has a dimension.
Deleted UserAugust 11, 2024 at 07:07#9243970 likes
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javi2541997October 12, 2024 at 12:49#9390050 likes
New rules: A pot is stored on the shelf. To the pot there are other pots as well. All of them have the same size, weight, shape, and colour. Each pot contains the same proportion of whatever thing. They are located in the third step, so if one falls down, it gets broken. You are cooking (edit: dressing) Greek salad in your kitchen, but you notice that there isn't enough honey, so you ask your sister—who is a crackpot—to go to the pots and take some honey for the delicious salad that you are cooking up. When your sister enters the saloon, you hear a clatter sound, and your sister shouts, 'Ouch!'
How many pots got cracked considering there is already +1 crackpot and the rest of the pots are equivalent?
Reply to javi2541997 pretty sure the cracked pots are an exponential function such that if you allow 3 or 4 it's containable, but 6 or 7 might make all the non-crackpots become pots that can be cracked.
F(x) = x^C where "C" is the cardinality of the set of "pots"
javi2541997October 12, 2024 at 18:36#9391000 likes
but 6 or 7 might make all the non-crackpots become pots that can be cracked.
That is probably one of the best phrases I read here so far.
If only the sister wasn't a crackpot, the only pots susceptible to being cracked were the ones on the shelf. Everything here is very complex and tricky. Who is responsible for the cracking? The crackpot sister or the pots on the shelf? I am starting to think that they are opposite poles. Their orbital gravitating force only led them to the destruction. :sad:
Comments (101)
Math rules are discovered, not made.
You start with it and anything added is left behind at the end.
If it is going to be discovered, then it is covered...
And hence, it is.
Where are mathematical expressions before they are discovered?
The simple answer - they are not discovered.
That shows a lack of imagination.
So, do you choose inconsistency, or reject John Gill's formulation?
There may be a way around the inconsistency.
So we have, from @John Gill,
For any two integers a,b, a+b=0
And we have from you,
For any two integers a,b, ab = ?
(The italics indicate the special in-game nature of the word 'integer').
Now ab is just a+a+a..., b times. But substituting a for b in John's rule, a+a=0
Hence, skipping a bit, 0=?.
And hence, a+b = ?
We might treat this as a definition of integer, such that an integer is any number that, added to another integer, yields ?.
It's credentials as such should be evident in the content.
Also, extending the game is dependent on creativity - and hence on a large number of folk participating.
The contention here is that this game has similarities to mathematics, in that the playful creation of rules is at the core of both.
Since it is clear that this game is constructed, not discovered, the game is a rejection by example of the doctrine set out here: Quoting frank
My rule is that they are discovered. Don't toss away my rule because of some made-up logic.
I add that there exists Absolute Infinity.
Is then ? absolute infinity or not?
(I like Banno's game :up: )
I'm tossing it away because it is silly.
Quoting Pfhorrest
hence we might presume a number bigger than the first number bigger than any integer.
What does bigger look like here?
Math games with arbitrary rules are a useful waste of time. If you really want rules, reality has some for you. For math or language to really be of any use, they need to inform and predict the world as it was, is and will be.
A GIll Integer differs from other integers in that when summed, they add to zero.
Now, is there more than one Gill Integer?
Let's call them Fhorrest Integers.
Are they the same as Gill integers?
No. You're tossing it away for no reason.
(This will lead to a pathological nightmare in the case of an uncountable infinity of such sets)
The Axiom of Inclusion: Given two empty sets, one is the absence of an element of the other.
:nerd:
Me???
:lol:
Surely you jest. Maths are beyond my understanding. I don't want to be a bullshitter!
:wink:
I'll watch. Have fun.
Some rules lead to a more interesting game.
The preference for consistency is one such rule.
Let's go back to their origins. How did humans come up with arithmetic? Probably when it became useful to track transactions and taxation. And that's not arbitrary.
Hmmm. Now where did we come up with a number system base 10?
Quoting Banno
Are my two axioms inconsistent? :roll:
So let's try this out. I as ruler of the nearby city demand you pay a tax. I have my soldiers take three oxen out of your six. You complain that this only leaves three oxen to plow the fields. My official reply is that six minus three is five, by decree. I have only removed one of your oxen.
For some reason, that system doesn't last and is replaced by the 6 - 3 = 3 one we have today.
Right, so is math about useful patterns, or about making up arbitrary games, like Chess and Go are made-up games with well defined rules that allow for interesting patterns?
Or maybe both.
Shades of Heraclitus?
That’s part of the point of this approach.
I don't mind your inconsistency. It is like the food I cook for my children... it has a certain uncertain flavour peppered with a consistency of indescribable inconsistency.
At least we are consistent about this.
So, the world-stuff creates patterns that we sometimes find useful and turn into mathematics and physics.
That says more about the world than is needed.
Stuff does stuff. We make patterns. Sometimes we read patterns into what the stuff is doing.
Less metaphysics. .
What are 'integers' in your game? The way integers are usually defined/constructed, they come with addition already baked in.
Thats why I proposed the rule that Banno hand over 50% of his dough. I thought we should start where the ancients did when the rules were meant to be applicable in the world.
Useful for what? Why is a pattern useful?
And if you discover what's not silly, where was it before you found it?
Merry Christmas! :sparkle:
Happy Holidays! :nerd:
I think I have to pay that.
SO maths is made up, and we find - "discover" - ways to use it.
Whatever you like.
Sometimes we impose.
Could be.
Quoting Banno
How is 3+3=6 useful for knowing how much of my income the government wants? If the government wants 50% of my income, do I just write 50% on a sheet of paper and then give it to the government? Are we just writing scribbles with arbitrary rules? If so, then why isn't the government content with a sheet of paper with the scribbles 50% on it? What is 50% OF something? What does the "of" mean?
Quoting Banno
The symbols are made up, but what they refer to isn't.
All rules prior to this post are not to be followed after this post.
All posts ought to follow the rule: share your favorite (philosopher, artist, food, or quote)
Contradiction!
Proof:
Quoting jgill
Quoting I like sushi
Quoting Deleted user
Every contradiction shall be resolved both ways.
Then surely the sum of any two integers is 0, and we must accept that two rules can be combined and that all can be used more than once
Or we must never reference a previous rule to even your post, and the sum of any two integers is the sum as we understand it from the textbooks.
And, having said this, the first is the assertion, the second the negation, and now I'm wondering -- what's the negation of the negation?
Always "and", and never "or", but also "or"... Etc.
Banno's thesis is that maths is invented, not discovered, just as games like chess are. Well then it is very easy to invent some rules for a game or some rules for a mathematics, and there are lots of them. But most are dull or unplayable.
So the thread itself is badly set up as a game that doesn't have much interest or significance, because posters can, and nearly always do, take the nuclear option and pretend they have "won". A better win might be if we could come up with a new form that was consistent and incomplete, but not isomorphic with arithmetic or something like that. I don't have a better set up that would encourage that, unfortunately.
Me either.
Though I think your insight here is worth preserving:
Quoting unenlightened
The nuclear option -- contradiction -- is something like the fruit on the tree in paradise?
This, though, is the stronger point.
If the King is in check then the other player can swipe away the peices, but this is rude (and so it goes with the other games; the dull and unplayable games seem to proliferate, and the interesting ones are the ones we ought go for)
I think math is probably like chess, but that chess was built upon mathematics: so the metaphor is good, but starts on the wrong side.
Quoting unenlightened
And yet it lives, five years on.
Quoting Moliere
Some rules ruin the game, others make it more interesting.
One way to fix the game might be to oblige players to list the rules they are making use of, and hence have them construct a tree.
Hence,
Quoting Banno
Quoting jgill
Quoting Pfhorrest
Quoting Banno
Conclusion: Quoting Banno
Quoting Banno
Quoting Banno
Question: prove that Fhorrest integers are the same as Gill integers
Quoting Deleted user (from JGill's rule)
Conclusion: Quoting Deleted user
An adding: If there is only one integer, then Fhorrest integers are the same as Gill integers.
New rule: There is an integer that is neither a Fhorrest integers nor a Gill integer.
Your turn...
That might be (but actually isn't) an interesting game, but it is no longer chess. Allegedly, rugby was invented when some idiot was supposedly playing football and picked the ball up and ran with it. A few other things had to change before it became a game worth playing.
There is a card game called "52 card pick up", in which the dealer throws all the cards up in the air, and leaves their opponent to pick them up. It's faintly amusing. Once.
Quoting Banno
As does 52 card pick up. But if you want to do something interesting in mathematics, or the philosophy of mathematics, this is not the way to go about it.
But yet again, here you are…. :wink:
(FWIW though, my name isn't P. Fhorrest, it's just Forrest but spelled with a Pfh instead of an F).
I'll admit that that's not my favorite game. And there are only so many times I can play it.
Though what becomes shit was at one point food
Quoting Deleted user
Hrm. What's it derived from? "How does math work?" ?
What of us who think it is both created and discovered?
Quoting jgill
Quoting Pfhorrest
It must be a number smaller than omega, but not zero.
Something like this: x (the suspicious integer) < ?.
It is 1. Why? Because it is the smallest integer greater than zero and the smallest of Omega.
Everything I wrote above is pure crank, right? :lol:
It is a bit fuzzy. But here is an example: Linear fractional transformations have been around for years but at some point someone discovered they could be categorized by the behavior of their fixed points. One such categorization was "parabolic", in which the fixed point demonstrates both attracting and repelling behaviors. Thus, a category was both discovered and created. When I determined the conditions under which infinite compositions of parabolic transformations converge to their fixed points years ago that was a discovery based upon a creation.
And speaking of which, category theory could be considered a creation, then its characteristics follow as discoveries.
However, I am open to other perspectives. Most mathematicians don't care to argue the point. But it is certainly fair game for the philosophically inclined.
Been a long time buddy. Come back to the forum! It needs all the rationality it can get at this moment in history :lol:
They believe I am trolling, but I simply lack wording and reasoning.
New rule: The sum of the product of any two integers is omega minus (now corrected!) the double of Lionino’s integers.
I think that the distinction between creation and discovery only applies to concrete things, and for abstract things like mathematics there is no such distinction. Because there we're dealing entirely with matters of possibility, so to discover something is just to show that it is possible, as in, it could be created, at any time; and conversely, to create something is only to show, and so discover, that it is possible, and always has been.
It's only with concrete things that exist within time that they could have already been actualized (in the past) and so be available to be discovered, in a way distinct from not having been actualized yet and so being available to create (in the future).
It turns to an uncountable dimension. Right? Or am I lost in something?
Now, I can't see the next step in your rule.
I think I can see it. By uncountable in your definition, it means that there are infinite subspaces or dimensions. Right? It is not about to be countable but if the vector space has a dimension.
How many pots got cracked considering there is already +1 crackpot and the rest of the pots are equivalent?
Please, elaborate.
Something closer to this:
F(x) = x^C where "C" is the cardinality of the set of "pots"
That is probably one of the best phrases I read here so far.
If only the sister wasn't a crackpot, the only pots susceptible to being cracked were the ones on the shelf. Everything here is very complex and tricky. Who is responsible for the cracking? The crackpot sister or the pots on the shelf? I am starting to think that they are opposite poles. Their orbital gravitating force only led them to the destruction. :sad:
Wait... cooking a Greek Salad...?
OK... OK... sorry, my bad. You are dressing the Greek salad...
So, the counting of cracked pots starts at zero and not one.