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gbesq
·Sorry, you can’t have that! If the applications were there, discovered, surely? Binary answers only, this is the internet.😉
The OF Clubhouse Water Cooler
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p4ul
·And to really stir the pot, surely your God created mathematics? Just need to work in some politics to completely burn this thread.
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The Father
·You all are much smarter than me. But human biology is amazing. I am always stunned how complex the human body is. Complex and delicate balance of “stuff” that makes it work. Anyway that is my contribution to the cooler
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gbesq
·And to really stir the pot, surely your God created mathematics? Just need to work in some politics to completely burn this thread.
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p4ul
·
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p4ul
·I'll make it even worse. I'm an agnostic, so maybe God exists and he/she/it created mathematical constructs or maybe God doesn't exist and the universe is just the way it is. Besides, would an all knowing, all loving God tolerate a planet that has TWO systems of weights and measures? I think not.
Might be worth asking some knowledgeable Australian philosOFers?
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wagudc
·I'm firmly in the camp that math is invented by humans. It is a model of reality, not reality itself. Look up Gabriel's Horn paradox or the Banach-Tarski paradox.
Gabriel's Horn is a particular infinitely long straight trumpet and it is possible to prove that it has finite volume but infinite surface area. It requites an infinite amount of paint to paint the outer or inner surfaces of the horn (it has no thickness). However, because the volume is finite, it is possible to fill the horn with paint. Once you dump out the paint, have you not painted the inner surface?
The Banach-Tarski Paradox says that it is possible to take a solid sphere, break it up into parts, and then reassemble them into two solid spheres of the exact same size as the original. It is possible to prove this without much difficulty, but one cannot do this in reality because the disassembly would require an unaccountably infinite number of impossibly complex cuts.
Also, many aspects of mathematics are arbitrary, it could have been invented in other ways. Although the differences would mostly be inconsequential.
Gabriel's Horn is a particular infinitely long straight trumpet and it is possible to prove that it has finite volume but infinite surface area. It requites an infinite amount of paint to paint the outer or inner surfaces of the horn (it has no thickness). However, because the volume is finite, it is possible to fill the horn with paint. Once you dump out the paint, have you not painted the inner surface?
The Banach-Tarski Paradox says that it is possible to take a solid sphere, break it up into parts, and then reassemble them into two solid spheres of the exact same size as the original. It is possible to prove this without much difficulty, but one cannot do this in reality because the disassembly would require an unaccountably infinite number of impossibly complex cuts.
Also, many aspects of mathematics are arbitrary, it could have been invented in other ways. Although the differences would mostly be inconsequential.
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Peemacgee
··Purrrr-veyor of luxury cat box loungersI'll make it even worse. I'm an agnostic, so maybe God exists and he/she/it created mathematical constructs or maybe God doesn't exist and the universe is just the way it is. Besides, would an all knowing, all loving God tolerate a planet that has TWO systems of weights and measures? I think not.
Just two?!!
Have you met our Indian brethren?
Lakhs anybody?
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p4ul
·I'm firmly in the camp that math is invented by humans. It is a model of reality, not reality itself. Look up Gabriel's Horn paradox or the Banach-Tarski paradox.
Gabriel's Horn is a particular infinitely long straight trumpet and it is possible to prove that it has finite volume but infinite surface area. It requites an infinite amount of paint to paint the outer or inner surfaces of the horn (it has no thickness). However, because the volume is finite, it is possible to fill the horn with paint. Once you dump out the paint, have you not painted the inner surface?
The Banach-Tarski Paradox says that it is possible to take a solid sphere, break it up into parts, and then reassemble them into two solid spheres of the exact same size as the original. It is possible to prove this without much difficulty, but one cannot do this in reality because the disassembly would require an unaccountably infinite number of impossibly complex cuts.
Also, many aspects of mathematics are arbitrary, it could have been invented in other ways. Although the differences would mostly be inconsequential.
Your argument would have been perfect if only you had spelt ‘math’ correctly, it is maths.😗
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gbesq
·Another take on the subject: Pythagoras’ revenge: humans didn’t invent mathematics, it’s what the world is made of (theconversation.com)
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RevZMan123
·Who has a good meatloaf recipe that they want to share?
2.5 pounds ground meatloaf mix (equal parts ground beef, pork and veal or turkey)
1 2/3 cup dried breadcrumbs 140g
3 1/3 tablespoons chopped fresh flat-leaf parsley or 1T dried parsley
3 large eggs, lightly beaten
1 large onion, grated
2 clove garlic, minced
3/4 cup ketchup
1 2/3 tablespoon plus 1 1/3 teaspoon Worcestershire sauce
Kosher salt and freshly ground black pepper
3 1/3 teaspoons light brown sugar
Directions
- Preheat the oven to 350 degrees F. Line a rimmed baking sheet with parchment.
- Combine the meatloaf mix, breadcrumbs, parsley, eggs, onion, garlic, 1/2 of the ketchup, 1 2/3 tablespoon of the Worcestershire, 2 1/2 teaspoons salt and 3/4 teaspoon pepper in a large mixing bowl. Using your hands, mix together until well combined.
- Transfer the mixture to the prepared baking sheet and form it into a compact oval-shaped loaf about 9 inches by 5 inches. Bake the meatloaf for 30 minutes.
- Stir the brown sugar together with the remaining ketchup and Worcestershire in a small bowl for the glaze. Brush the top and sides of the meatloaf all over with the glaze. Return to the oven and bake until the glaze starts to caramelize and a thermometer inserted in the center of the meatloaf registers 160 degrees F, about 25 minutes more. Let rest for 10 minutes before slicing and serving.
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Dsloan
·I'm firmly in the camp that math is invented by humans. It is a model of reality, not reality itself. Look up Gabriel's Horn paradox or the Banach-Tarski paradox.
Gabriel's Horn is a particular infinitely long straight trumpet and it is possible to prove that it has finite volume but infinite surface area. It requires an infinite amount of paint to paint the outer or inner surfaces of the horn (it has no thickness). However, because the volume is finite, it is possible to fill the horn with paint. Once you dump out the paint, have you not painted the inner surface?
The Banach-Tarski Paradox says that it is possible to take a solid sphere, break it up into parts, and then reassemble them into two solid spheres of the exact same size as the original. It is possible to prove this without much difficulty, but one cannot do this in reality because the disassembly would require an unaccountably infinite number of impossibly complex cuts.
Also, many aspects of mathematics are arbitrary, it could have been invented in other ways. Although the differences would mostly be inconsequential.
Do you have any book/podcast/video recommendations on this topic? As a layperson with an odd interest in epistemology and philosophy, I find this all very interesting. To me, math has always seemed like a great window through which to examine the way that our brains construct our experience of the world. Math can seem to so fundamentally or objectively describe the world, yet as you note, there's slippage between reality and math that points to it being a set of linguistic tools. And, I also find it fascinating how things like math and writing are relatively new human inventions, yet our brains seem so primed to be able to make use of them - and they are so fundamental to our experience of the world.
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hen
·Happy international womens day everybody.
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wagudc
·Another take on the subject: Pythagoras’ revenge: humans didn’t invent mathematics, it’s what the world is made of (theconversation.com)
One can discover mathematical concepts in nature, but I disagree that all of mathematics is pre-existing waiting to be discovered. I would also argue that Gödel's completeness theorem proves that all of reality is mathematical. It says that you cannot prove everything from any finite set of axioms. Thus to understand the world mathematically, you would need to have an infinite set of basic assumptions.
Edit: I should add that this is my perspective as one applied mathematician. There is certainly room for both perspectives among mathematicians.
Edited:
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wagudc
·Do you have any book/podcast/video recommendations on this topic? As a layperson with an odd interest in epistemology and philosophy, I find this all very interesting. To me, math has always seemed like a great window through which to examine the way that our brains construct our experience of the world. Math can seem to so fundamentally or objectively describe the world, yet as you note, there's slippage between reality and math that points to it being a set of linguistic tools. And, I also find it fascinating how things like math and writing are relatively new human inventions, yet our brains seem so primed to be able to make use of them - and they are so fundamental to our experience of the world.
This video gives a good lay person's intro to set theory and the Banach-Tarski paradox and is quite good in my opinion.
Gabriel's Horn Paradox requires some knowledge of Calculus, I don't see how to understand it without a basic knowledge of Calculus. This video explains it. @p4ul will be happy with it, the guy in the video is a Brit and says "maths"
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Dsloan
·This video gives a good lay person's intro to set theory and the Banach-Tarski paradox and is quite good in my opinion.
Gabriel's Horn Paradox requires some knowledge of Calculus, I don't see how to understand it without a basic knowledge of Calculus. This video explains it. @p4ul will be happy with it, the guy in the video is a Brit and says "maths"
Thanks! Luckily, I got a 5 in AP calc many years ago, so... I think I get it, sort of!
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ahartfie
··The black sheep in the Spee-ee-eee-eedmaster flockWho has a good meatloaf recipe that they want to share?
~3 pounds meat. I like to use two of the meatloaf mix packs and those are usually around 1.3 pounds
2 eggs
1 envelope onion soup mix
1 cup whole milk
A few good glugs of Worcestershire sauce
~1 cup dried bread crumbs
Glaze: even amounts of, usually about 1/3 cup each
Ketchup
Yellow mustard
Brown sugar
Method:
Beat eggs and add milk. Add onion soup mix to hydrate and add Worcestershire sauce. Let sit for a few minutes.
Break up meat with hands, add egg/milk mixture, and combine thoroughly. Add enough breadcrumbs so that the mixture binds together. You may not need the whole cup, or you may need more.
Put onto a parchment or foil-lined sheet and form into loaf.
Brush with glaze.
Bake at 350 for 60-75 minutes or until it’s done how you like it. You can also form it into smaller loaves which will cook faster.
Let sit for 10 minutes out of the oven.
Slice and enjoy.
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gbesq
·I love this thread. The origin of mathematics, the universe and meatloaf recipes all in one place. Life is good.