The unreasonable effectiveness of mathematics

[blü 2]

This is because math is a logic-based language. Human languages don't exist outside the brains of humans and other animals that can understand it. And just as humam language is, there isn't only one way to do it and even other animals have their own languages, including some that have been observed using their own version f math.

Or what we take to be maths. But yes, it seems that all critters have evolved to interpret their world as categories, even at such basis levels as "particular sensory input, particular response" which may not require thought as such but rather stimulus-response eg spider 'knowing' it's caught a fly in a web, fish 'knowing' that image is food, and so on.

 

[Enai de a lukal]

Maths is purely conceptual, a tool we use for organizing our perceptions of reality.


Where else do you say it exists, other than as concepts in a human brain?


No, it doesn't have a quantity until you choose to interpret it in terms of quantity. Maths is the human-made map, not the objective territory. Without humans there are no plants, trees, flowers, grass, grain, no mountains or hills, no bees, spiders, fish, birds, animals, just aggregates of things.

If you've ever watched babies learning to talk, you'll see how we're geared to think in categories because that works for us. We impose form on the world. It has none of its own.


I disagree. There's no such thing as collections, categories, examples, unless you, the observer, choose to see things that way. Which we've evolved to do. so from a survival point of view that approach works.


Not unless and until YOU decide (as you've evolved to do) that this thing is a monkey and this thing is a grub and this thing is a grub and this thing is a hand and this thing is a hand and this thing is a grub and this thing is a grub.


Again, we've evolved to categorize the world. In our absence the world simply is.


Mathematical platonism requires belief that maths exists independently of our concepts of maths, ie independently of humans, but does not exist materially. Therefore it exists somehow in Platoland, an alternative universe somehow overlapping ours; and Platoland is a notion I reject.

So these things jump into existence when humans are paying attention to them, but then disappear the moment we look away? Uh, no. The three trees in my yard remain in existence, and retain the quantity of 3, all day long whether I"m looking at them or not.

And once again, there are realist positions wrt ontology- that is, the view that mathematical objects and truths exist independently of humans- that are not Platonic, do not involve Platonic Ideas living in abstract PlatoLand. You are, apparently, completely out of the loop.

 

[blü 2]

So these things jump into existence when humans are paying attention to them, but then disappear the moment we look away? Uh, no. The three trees in my yard remain in existence, and retain the quantity of 3, all day long whether I"m looking at them or not.

This interpretation of them exists as concepts in a human brain, yes. No human brains, no maths.

And once again, there are realist positions wrt ontology- that is, the view that mathematical objects and truths exist independently of humans- that are not Platonic, do not involve Platonic Ideas living in abstract PlatoLand. You are, apparently, completely out of the loop.

Please explain the manner in which E=mc^2 "exists" when no brain is around to hold the concept (and the concepts involved in that concept).

 

[Enai de a lukal]

We're not talking about interpretations, but trees. There are three trees in my yard, regardless of whether I'm conceptualizing the number 3. There are 3 trees in my yard, even when no one is home. IF tomorrow the entire human race were to go extinct there would still be trees in my yard, and they would still be 3.

And energy is still equivalent to mass times c squared, regardless of whether there are any brains around. Are you seriously suggesting the phenomena this equation describes ceases to hold when there are no brains around to hold the concept? Was E not equal to mc-squared prior to Einstein's discovery of the formula? The position you're staking out is absurd.

 

[Ostronomos]

We're not talking about interpretations, but trees. There are three trees in my yard, regardless of whether I'm conceptualizing the number 3. There are 3 trees in my yard, even when no one is home. IF tomorrow the entire human race were to go extinct there would still be trees in my yard, and they would still be 3.

Allow me to point out the flaw in your logic. The trees become merely an assumption when they are not being looked at. Observation or consciousness creates reality. When you die, the information within your brain is downloaded into the universal quantum computer. Consciousness IOW, continues after death.

And energy is still equivalent to mass times c squared, regardless of whether there are any brains around. Are you seriously suggesting the phenomena this equation describes ceases to hold when there are no brains around to hold the concept? Was E not equal to mc-squared prior to Einstein's discovery of the formula? The position you're staking out is absurd.

Your comment only serves to reinforce the view that mathematics is inherent to reality. Any opinion to the contrary is absurd.

 

[Enai de a lukal]

The trees become merely an assumption when they are not being looked at. Observation or consciousness creates reality. When you die, the information within your brain is downloaded into the universal quantum computer. Consciousness IOW, continues after death.

I'm sorry but this is just naked woo.

 

[Ostronomos]

I'm sorry but this is just naked woo.

If by "woo" you are merely indicating that you disagree based on the imperfections in my statement then that is all fine and dandy. However, if you intend to dismiss that facts about the after-life then that "woo" is dishonest.

 

[Enai de a lukal]

If by "woo" you are merely indicating that you disagree based on the imperfections in my statement then that is all fine and dandy. However, if you intend to dismiss that facts about the after-life then that "woo" is dishonest.

It means what you said is silly quantum woo and I'm not interested in the amount of effort required to correct it. I'm not here to give you Remedial Quantum Physics 101.

 

[Twilight Hue]

Animals could never understand the human's perception of numeration, period.

That not entirely true.

More Animals Seem to Have Some Ability to Count

Counting may be innate in many species

www.scientificamerican.com

There were cases mentioned in Scientific American where monkeys could outperform college students under certain conditions.

 

[Comradio251]

That not entirely true.

More Animals Seem to Have Some Ability to Count

Counting may be innate in many species

www.scientificamerican.com

There were cases mentioned in Scientific American where monkeys could outperform college students under certain conditions.

Monkeys can do math the same way pigeons do math. But it's not the way humans do math. Plus, humans are testing their capabilities with our already perceived understanding of numbers and arithimetic. Humans created numbers not monkeys or any other animals for that matter.

https://www.npr.org/sections/thetwo...just-as-good-as-monkeys-when-it-comes-to-math

"While this is obviously a long way away from how humans can count, it shows that an animal with a brain structured quite differently to ours is still able to perform complex mental tasks of which only humans were once thought capable," said Scarf."

So my point still stands. Monkeys are approximators but they still fail to do basic math the way we do it like addition and subtraction. They approximate most of the math they test on them and they still get it wrong a lot of the time; https://www.science.org/content/article/monkeys-can-do-math

But when Livingstone and colleagues started analyzing the data in more detail—they had the results of hundreds of tests per day for months on end—they realized that the monkeys weren't 100% accurate. They tended to underestimate a sum compared with a single symbol when the two were close in value—sometimes choosing, for example, a 13 over the sum of eight and six. The underestimation was systematic—when adding two numbers, the monkeys always paid attention to the larger of the two, and then added only a fraction of the smaller number to it.

No, monkeys are not as good at math as you are lead to believe. The more the scientific data is analyzed the more the general consensus changes. I don't just read headlines to articles either.

 

[Shadow Wolf]

There were cases mentioned in Scientific American where monkeys could outperform college students under certain conditions.

Damn, people are so stupid I can't even compare them to monkeys anymore.

 

[Comradio251]

Here is more clear scientific evidence per the data to substantiate my argument that monkeys do not count like humans. It's probably the clearest example.

Mathematical brains — an excerpt from ‘Seeing the Mind’

First analysis:

First finding: After some training, the monkeys performed this task remarkably well. They succeeded with a great variety of configurations, and could clearly focus solely on number. Their only problem was to answer “same” when the two numbers were close, like 4 and 5. Thus, monkeys cannot count but can only estimate an approximate quantity of items.

These certain Macaque monkeys cannot differentiate between 4 and 5 objects. Thus, they cannot count like us but approximate instead.

Second analysis explains why these monkeys cannot count based on their wiring:

The macaque brain contains neurons tuned to number. Each of these cells responds to a certain number of objects. Some fire only when the animal sees one object; others prefer two; still others are stimulated by seeing three, four, or five objects. Each neuron possesses a favorite number, but their tuning is not perfectly sharp: Neurons that fire the most to four objects, for example, also respond to three or five objects. Again, monkeys’ number sense is approximate.

The conclusion is... they don't count like humans. But approximate like I already said.

Don't bet on a monkey to do 'actual' basic college math like Algebra II also. Yes, truly, if you believe that monkeys are smarter than college students you are extremely naïve.

Mental addition is for pre schoolers and no, college students still did better than monkeys at basic mental addition 94 percent ~ college vs 76 percent ~ macaque. **mod edit**

 

[Twilight Hue]

Monkeys can do math the same way pigeons do math. But it's not the way humans do math. Plus, humans are testing their capabilities with our already perceived understanding of numbers and arithimetic. Humans created numbers not monkeys or any other animals for that matter.

https://www.npr.org/sections/thetwo...just-as-good-as-monkeys-when-it-comes-to-math




So my point still stands. Monkeys are approximators but they still fail to do basic math the way we do it like addition and subtraction. They approximate most of the math they test on them and they still get it wrong a lot of the time; https://www.science.org/content/article/monkeys-can-do-math


No, monkeys are not as good at math as you are lead to believe. The more the scientific data is analyzed the more the general consensus changes. I don't just read headlines to articles either.

I would love to see you to outperform one of those monkeys.

 

[Comradio251]

I would love to see you to outperform one of those monkeys.

Reported for ad hominem attack. You lost the debate too.