The word "finger" did not occur so I skipped it.
"Please don't post shallow dismissals, especially of other people's work. A good critical comment teaches us something."
How inevitable is the concept of numbers?
71–80 of 211 posts
Re: How inevitable is the concept of numbers?
#72NASA found it simpler to explain numbers with hydrogen atoms than peano arithmetic for their voyager.
Does "easier" equate to "universal". I think it does, just thinking about your statement out loud.
Since to humans, explaining numbers with hydrogen would be harder, I think. The common ground between humans is larger, so we can rely on something less fundamental and abstract.
Re: How inevitable is the concept of numbers?
#73I like that he keeps it open-minded, but I've thought a lot about this and to me the case for numbers being inevitable is decisively yes. Every adaptable system evolves to adapt to a changing environment by detecting "modes" (categories) and adapting to each mode. Then we start noticing categories come in instances. There's a tree, there are more trees. So now it's useful to count them... Then it's useful to have fra…
Your argument is tautological.
Do we really know if adaptation is responding to discrete classifications of environmental pressure?
There could be other ways to describe how systems adapt. You are ascribing a lot to how you think it emerged.
I think your opinions are great, but I just have a hard time having beliefs about things that are as fundamental as numbers.
Re: How inevitable is the concept of numbers?
#74My guess is that the aliens of which Wolfram speaks would know about numbers. After all, animals do (see e.g. https://www.bbc.com/future/article/20121128-animals-that-can... ).
What if that's only a feature of animals that went through biological evolution on earth?
Re: How inevitable is the concept of numbers?
#75‘If a lion could speak, we could not understand him’. - Wittgenstein So even things we understand as fundamental truths of the universe are so deeply rooted in human experience that it's possible another living entity could be so different than ourselves that the capacity to sympathize with one another about certain things may simply not exist. Would a lion understand a corsage? Would an alien know what 12 x 12 means…
Related to this I have often wondered if childhood amnesia is (by a crude analogy) a "format problem".
In this analogy, the lion is our younger selves. Perhaps our brain changes so much that we cannot understand (or access) what we were thinking or experiencing anymore.
If we imagine that long term memories are encoded in a way that they can later be interpreted actively by the structures of the brain, we could expect that major developmental changes in brain function might impact the ability to interpret long term memory formed before the change.
Physical trauma, the major reorganisations of infancy and language acquisition all prompt changes in organisation and processing that could be what renders earlier memories inaccessible.
This (admittedly hand-wavey) idea seems to mesh well well with the observed details of the phenomenon. Frequently accessed memories may be re-encoded, leading to some continuity. Children themselves experience fairly continuous long-term memory. Types of memories where relevant processing might not have changed as much (smell, visual memory) might be more resilient. We would expect age of language acquisition to play a part. Etc.
Re: How inevitable is the concept of numbers?
#76Earlier quoted context omitted.
Because multiplication is just the number of times you add something to 0. If you add 2 to 0 3 times you get 6, if you add 2 to 0 0 times you get zero.
I’ve mentioned in a comment above, I find nothing natural in doing operations related to zero i.e. related to nothingness, meaning that I see “adding” and “zero times” as an oxymoron (you cannot associate an action, “adding”, to nothingness, i.e. to “zero”).
> I find nothing natural in doing operations related to zero i.e. related to nothingness, meaning that I see “adding” and “zero times” as an oxymoron (you cannot associate an action, “adding”, to nothingness, i.e. to “zero”).
Seems related to [this problem](https://stackoverflow.com/questions/47783926/why-are-loops-a...).
This is, a proper loop is like
do while (condition)
{
// ... body ....
}
do
{
// ... body ....
}
while (condition)
if (!zero)
{
do
{
// ... body ....
}
while (condition)
}
Re: How inevitable is the concept of numbers?
#77Arguably, number came from money. Not just the counting, but the generalization/fungibility - money can be exchanged for anything (unlike barter); number can represent a quantity of anything.
Trade and money have more direct survival advantages than number, an evolutionary gradient for improving the cognitive capacity supporting this generalization
Re: How inevitable is the concept of numbers?
#78Earlier quoted context omitted.
Because multiplication is just the number of times you add something to 0. If you add 2 to 0 3 times you get 6, if you add 2 to 0 0 times you get zero.
I’ve mentioned in a comment above, I find nothing natural in doing operations related to zero i.e. related to nothingness, meaning that I see “adding” and “zero times” as an oxymoron (you cannot associate an action, “adding”, to nothingness, i.e. to “zero”).
I think historically there were a number of cultures who had trouble with the mathematical concept of zero, so it's not universal
Re: How inevitable is the concept of numbers?
#79Arguably, number came from money. Not just the counting, but the generalization/fungibility - money can be exchanged for anything (unlike barter); number can represent a quantity of anything. Trade and money have more direct survival advantages than number, an evolutionary gradient for improving the cognitive capacity supporting this generalization
Shouldn't language predate money?
Language or cave paintings or whatever, use discrete symbols to describe physical reality
Re: How inevitable is the concept of numbers?
#80Numbers is the consequence of conservation law. If you relax the definition of the natural number as something that can be stable at time and space, you will see another system is possible. Gosh, even periodic table is a good example of what is possible if no strict proton-oriented association is in mind.