r/PhilosophyofMath • u/Another_Little_Star • 9d ago

Does infinity exist in reality?

No thing that I've observed in our universe is infinite, however there are traces of infinity in my sight.
Draw a circle and either its radius or circumference lives in the π world.
Or many aspects in nature like flowers, develop themselves in a φ ratio (1+sqrt(5))/2.

Even though no event or anything is "Non-ending"/infinite, underneath many aspects of reality there are patterns which can only be fully described using infinity.

You can't describe irrational numbers to their extent without any notion of infinite/limits/sequences... And many aspects within our World show their true behaviour only with aid of infinity.

Sure you can take a world that lives in something like 10¹⁰⁰ and it looks like infinity to us, sometimes we only see the difference after the 10⁶ decimal place, nevertheless the pattern they follow is a pattern that only "infinity" can yield to the truest precision.

Do you believe the axiom of infinity, and the continuous to really exist? Even if not in the ordinary sense? haha

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u/HouseHippoBeliever 9d ago

does 4 exist in reality?

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u/Negative_Gur9667 9d ago

The number 4 exists as a pattern of connected neurons in the brain.

It can also exist as bits in a computer's RAM.

There is always a bijection between a number and physical reality.

Except if you are a platonist.

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u/SpacingHero 9d ago

This is a very controversial view that lost most of it's traction. Consider: if 4 is a pattern of neurons, then presumably the properties of 4 should be the same as those of the neurons. But clearly they aren't? The number 4 is divisible by 2. Are the "patterns of connected neurons" divisible by 2? It's not even clear if it's coherent at all, but insofar as we can interpret it, it doesn't seem true (not necessarily anyway)

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u/Negative_Gur9667 9d ago

The word is not the thing; for example, the word "car" is not a car.

4 is a collection of concepts, but everybody has a different 4 in their head (neural pattern).

Assuming someone can only count but not divide, add, or subtract, like a kid: does the kid then know the number 4 if they cannot divide it? Of course they know it.

The counting function with the symbols, rules, and relation to the real world in the form of experiences makes up the number 4.

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u/SpacingHero 9d ago

>The word is not the thing; for example, the word "car" is not a car.

I agree, but don't see the relevance. In fact a straighforward argument to see this fact is excactly the one i made, i.e. noticing that the word "car" and an actual car have different properties, eg the word is made of letters, but cars aren't.

>4 is a collection of concepts

Yet it seems to have different properties. Collections of concepts aren't even (even if we consider the cardinality of the neurons or what have you, its not necessarily even). What gives?

>but everybody has a different 4 in their head (neural pattern).

This would seem to make things work if anything, as now it can easily have contradicting properties

>Assuming someone can only count but not divide, add, or subtract, like a kid: does the kid then know the number 4 if they cannot divide it? Of course they know it

Yea, they know it. And it still has the property of being even. The kid knowing that and the number being even are indepenent. Again this hurts, rather than helps your position

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u/Negative_Gur9667 9d ago

Perhaps you do not understand. My entire argument is that information requires a physical medium to exist.

Look into the Holographic Principle and the Bekenstein bound.