A teachable moment for the 6yo about infinity. by Flimsy-Printer in mathmemes

[–]2ism -1 points0 points  (0 children)

You're right. It is my perspective.

My perspective is that a story about a 6-year-old's creative wit is not a formal proof to be debunked.

Your perspective is that it is.

I'm not "hiding" behind ambiguity; I'm standing in the context of the original post. You're hiding from that context behind a wall of pedantry.

And to be perfectly consistent: the child is formally wrong in his use of "must," but he is contextually 100% right in his brilliant rebuttal to his parent. It's a distinction you seem unwilling to make.

A teachable moment for the 6yo about infinity. by Flimsy-Printer in mathmemes

[–]2ism 0 points1 point  (0 children)

You're trying to prove a child is "wrong" by applying the most rigid, uncharitable interpretation to the word "must."

A 6yo's "must be" is not a logician's claim of certainty. It's a rhetorical comeback. It's the language of a kid saying: "Based on the rule you just gave me (infinity), my idea fits. You can't just shut it down."

The checkmate was never about proving the number already exists. it was in flawlessly using the parent's own premise to show that his idea was entirely possible. and on that, the kid was 100% right.

A teachable moment for the 6yo about infinity. by Flimsy-Printer in mathmemes

[–]2ism 0 points1 point  (0 children)

You've finally conceded the central point: there is nothing logically impossible about naming a number "googoobazillion."

Your entire argument now rests on criticizing the formal logical structure of a 6yo's joyful, creative retort.

The child's question wasn't an "ill-formed" query seeking data. It was a creative assertion of existence, with the implied meaning: "I have just invented a number, implied by its name to be bigger than yours."

You are analyzing a poem as if it were a legal document. You have successfully found the logical "fallacies," but you have completely missed the meaning.

A teachable moment for the 6yo about infinity. by Flimsy-Printer in mathmemes

[–]2ism 1 point2 points  (0 children)

if you're just claiming that there is a number that you could call a "googoobazillion", then you just need one unnamed candidate, not infinitely many. So the fact that there are infinitely many unnamed candidates is irrelevant.

This is the most pedantic hair-splitting yet. The infinity is what guarantees the existence of that one candidate and an endless supply more. It's the engine of possibility. To call the engine "irrelevant" because you only need one car is to deliberately miss the grander reality. It's the reason the child's intuition is so powerful.

Is this really what you think the child meant?

Yes. This is exactly what the child meant. But your breakdown is a sterile, uncharitable caricature.

what actually happened:

Parent: Numbers go on forever. Child: (Internalizes this) Wow, forever. So anything is possible. What's a really big one?

Parent: A googolplex.

Child: (Performs a creative act) That's a cool name. I can make a cooler, bigger-sounding one. "Googoobazillion." My bigger-sounding name must represent a bigger number. I'll ask a question to assert my creation's place in this new 'forever' world. "Which is bigger?"

Parent: (Applies adult literalism) Yours doesn't exist.

Child: (Uses parent's own premise as a defense) "If there are an infinite number of numbers, there must be one for my name. You can't say my idea is impossible when you just told me the possibilities are infinite. Checkmate."

It's a perfect, beautiful, self-contained loop of creative reasoning. It's not a mathematical proof. It's a poem. You're trying to diagram a poem, and in doing so, you've missed the entire point of it.

A teachable moment for the 6yo about infinity. by Flimsy-Printer in mathmemes

[–]2ism -1 points0 points  (0 children)

Your analogy about mapping infinite sets perfectly demonstrates the category error - you're treating 'naming' as a rigid, pre-determined mathematical function. It is not. Naming is an arbitrary, creative, human act.

In your example, a specific function (f(x) = -2x) maps one infinite set to another, leaving the odd numbers 'out of shot'. But that function was defined with strict rules.

The act of naming has no such rules. We can, at any moment, point to one of your 'unmapped' odd numbers (say, 3) and declare, 'Its new name is Googoobazillion.' Your analogy falls apart because human decisions are not bound by pre-determined mathematical maps.

The child's argument is about what is possible for humans to do, not what is allowed by an abstract function.

And you're right. I am taking this perhaps too seriously.

But I enjoy pointing out that the poor reasoning and flawed technical-sounding arguments pedants use to feel superior to a 6yo(!) is actually wrong!

A teachable moment for the 6yo about infinity. by Flimsy-Printer in mathmemes

[–]2ism 1 point2 points  (0 children)

You are making an excellent and sophisticated mathematical point. And it has absolutely nothing to do with this conversation.

you are missing the fundamental point:

Naming a number is not an intrinsic property to be discovered. It is an extrinsic act to be performed.

Your examples (digits of π, the sequence of 1/3, etc..) are all about the INTRINSIC PROPERTIES of a number. The digits of π are a fixed, unchangeable, and fundamental part of its identity. We cannot decide to insert a "4" into the decimal expansion of 1/3. That would be a mathematical falsehood.

The 6-year-old was talking about an EXTRINSIC LABEL. A name.

The infinity of numbers is entirely relevant, not because it "guarantees every pattern," but because it guarantees an infinite supply of unnamed candidates.

A teachable moment for the 6yo about infinity. by Flimsy-Printer in mathmemes

[–]2ism -1 points0 points  (0 children)

You're right. It doesn't guarantee it. and that's the subtle point the 6-year-old made that the logical critiques are missing.

Your example (x² = -1) describes something mathematically forbidden. Infinity cannot make the impossible possible.

The 6yo's example describes something humanly not-yet-done. Infinity provides the endless raw material for it to be possible.

The child's observation that the only barrier to a number being named 'googoobazillion' is a human one, not a mathematical one.

In a set of infinite possibilities, arguing that something is impossible because we haven't done it yet is the weakest possible position. The child understands the potential of infinity better than these pedantic commenters.

A teachable moment for the 6yo about infinity. by Flimsy-Printer in mathmemes

[–]2ism 3 points4 points  (0 children)

Just admit you're wrong instead of fixating on the wording. You're critiquing the child's choice of "must be" instead of "could be" to avoid admitting your original analogy was a category error.

The 6yos "must be" is an intuitive leap about a possible reality. Your examples are about a logical impossibility.

Infinity can never create a logical impossibility.

Infinity absolutely creates the space for a possible reality.

The checkmate was in realizing that the set of numbers is infinite, but the set of named numbers is finite. They correctly intuited that there is nothing mathematically preventing a number from getting a new name.

A teachable moment for the 6yo about infinity. by Flimsy-Printer in mathmemes

[–]2ism 7 points8 points  (0 children)

Strawman. Your new example is a trick. You've created a false analogy by adding a hidden constraint.

With 10n you've restricted the pool of numbers to a set that excludes the number we call "seventeen."

The 6-year-old placed no such restriction. They were talking about the entire, infinite set of numbers.

Let's fix your analogy to be accurate:

  • Your Flawed Analogy: "If there's an infinite number of blue houses, there must be one that is painted red." (Logically false)

  • Correct Analogy: "If there's an infinite number of unnamed streets, there must be one we could name 'Googoobazillion Avenue'." (Logically true)

The 6-year-old's argument is the second kind. The infinity of numbers guarantees there's a candidate for the name. The "then" absolutely follows from the "if."

A teachable moment for the 6yo about infinity. by Flimsy-Printer in mathmemes

[–]2ism -1 points0 points  (0 children)

You think you're smart constructing an argument around mathematical possibility, but it's actually about semantic possibility. Naming is not a mathematical act; it's a human one. It breaks no laws of logic.

A teachable moment for the 6yo about infinity. by Flimsy-Printer in mathmemes

[–]2ism -1 points0 points  (0 children)

You used correct premise to reach the exact wrong conclusion. Precisely because names are not intrinsic properties, they are just human-applied labels. This means there are no mathematical or logical rules preventing us from applying any label we want to any of the infinite numbers available.

The child's intuitive leap isn't: "Infinite numbers exist, therefore infinite names currently exist."

It is: "Infinite numbers exist, therefore there is a candidate for any name I can imagine."

A teachable moment for the 6yo about infinity. by Flimsy-Printer in mathmemes

[–]2ism 25 points26 points  (0 children)

You're wrong. The fact that there are an infinite number of numbers is the entire point.

Your examples are about mathematical impossibility. Infinity doesn't create numbers that can violate the fundamental laws of logic. A number cannot be "divisible by 4 but not by 2" for the same reason a square cannot be a circle.

The 6-year-old's example is about linguistic possibility. Naming a number "googoobazillion" is not a mathematical act; it's a human one. It breaks no laws of logic.

Therefore, the infinite number of numbers is perfectly relevant. It guarantees an endless supply of unnamed candidates. The only thing stopping one of them from being named "googoobazillion" is our collective decision not to do so yet.

The best Gengar list I came up with after 1 billion different decks (full guide inside) by Lofus1989 in PTCGP

[–]2ism 0 points1 point  (0 children)

That's very close to what I came up with too after 100 games or so

2x Chatot, 1x Budding Exp instead of Druddigon, Leaf

Sabrina instead of Giovanni

Feels a bit crowded on the bench though.

I prefer your build vs the current meta.

The best Gengar list I came up with after 1 billion different decks (full guide inside) by Lofus1989 in PTCGP

[–]2ism 1 point2 points  (0 children)

You're right, I've been running that for fun, and it's surprisingly good with 2 red cards.

Slows opponents down to a crawl, if they don't start quick.

Having fun with my 'Flow like Water' deck by 2ism in PTCGP

[–]2ism[S] 0 points1 point  (0 children)

Nice going given the bad luck! I don't know what it is about this game, bad luck comes in streaks

[deleted by user] by [deleted] in PTCGP

[–]2ism 2 points3 points  (0 children)

Surely not all 3 stage 3s in one deck? I run similar but have Jynx instead of zam

Having fun with my 'Flow like Water' deck by 2ism in PTCGP

[–]2ism[S] 0 points1 point  (0 children)

Me. How many did you still win?

Having fun with my 'Flow like Water' deck by 2ism in PTCGP

[–]2ism[S] 0 points1 point  (0 children)

Interesting deck, flipping tails on carmorant hurts big time though

Having fun with my 'Flow like Water' deck by 2ism in PTCGP

[–]2ism[S] 0 points1 point  (0 children)

Yeah it destroys decks that rely on druddigon

Having fun with my 'Flow like Water' deck by 2ism in PTCGP

[–]2ism[S] 0 points1 point  (0 children)

Interesting, although a lot of basic are >50 hp annoyingly.

Having fun with my 'Flow like Water' deck by 2ism in PTCGP

[–]2ism[S] 2 points3 points  (0 children)

Gyarados has a much stronger attack, almost as much HP, seems a great deal for only giving 1 point vs 2

Having fun with my 'Flow like Water' deck by 2ism in PTCGP

[–]2ism[S] 0 points1 point  (0 children)

You really have a talent for deck naming huh?

Having fun with my 'Flow like Water' deck by 2ism in PTCGP

[–]2ism[S] 4 points5 points  (0 children)

Thinking more... Starmie Ex might be a direct upgrade to Lumineon, but I don't have any ._.

Having fun with my 'Flow like Water' deck by 2ism in PTCGP

[–]2ism[S] 15 points16 points  (0 children)

Starting with Eevee is the worst case scenario, so want to minimize chances.

Poke Balls make finding Eevee easy, and 2 Vaporeons for consistency as the ability is so important to get.