What have been the greatest intellectual achievements? (2017) • Hacker News Board

Re: What have been the greatest intellectual achievements? (2017)

#91

Post by krapp » Mon, Apr 13, 2026, 11:05 PM UTC

vixen99 wrote: post #90

krapp wrote: post #88

Earlier quoted context omitted.

I ascribe the creation of God(s) to sub-rational behavior - paredolia, superstition, emotion born of fear and ignorance. The pinnacle of intellect was realizing the universe operated by rules that could be understood rather than the capricious will of supernatural forces.

If we've already reached the pinnacle I guess we've no more to achieve bar amassing a bunch more salient observations regarding how the universe ticks. The it's job done! Almost Boring.

I mean, this thread includes examples like agriculture and writing so I don't know why you're snarking at me specifically.

But all of modern science, including relativity (which is also mentioned somewhere) depends upon the initial insight that the natural world doesn't require supernatural explanation.

Re: What have been the greatest intellectual achievements? (2017)

#92

Post by [deleted] » Tue, Apr 14, 2026, 5:20 AM UTC

compounding_it wrote: post #3

Be modest. A lot was accomplished before you were born. Humans are incredible. Leaving the planet and taking a trip on the moon and possibly mars someday is no small feat. We just need to fix our planet. Or to be honest, stop ruining it so it heals itself.

[deleted]

Re: What have been the greatest intellectual achievements? (2017)

#93

Post by dtj1123 » Tue, Apr 14, 2026, 5:54 AM UTC

towledev wrote: post #87

dtj1123 wrote: post #67

Earlier quoted context omitted.

The difference is that zero is explicitly a number, rather than a concept. Making it a number allows it interact with the rest of mathematics in a consistent way, which I'd argue you can't do with "nothing". To use your later example of "no apples": Is no apples the same thing as no bananas? What about no meters? I honestly don't know, the question is a bad one. My gut says yes, nothing in each case is just nothing.…

Notably, zero persons have chosen to make the explicit case that zero is more ingenious than the Cartesian coordinate system. :)

Which is a better idea, the brick or the building?

Re: What have been the greatest intellectual achievements? (2017)

#94

Post by raddan » Tue, Apr 14, 2026, 4:57 PM UTC

finghin wrote: post #85

raddan wrote: post #59

Earlier quoted context omitted.

On the other hand, Leibniz was one of the very first philosophers who recognized the value of the unique combination of formal thinking and computation. There’s no doubt that he was one of the originators of the idea that calculation could be applied to general reasoning and not just arithmetic (although he also built a mechanical calculator, the “stepped reckoner”). Anyway, the following is one of my favorite Leibni…

Agreed! But he was not really pivotal in any application of those ideas, and realistically only had a hint of what they could be capable.

That is not correct. Leibniz’ work on calculating machines was hugely influential. [1]

[1] https://en.wikipedia.org/wiki/Leibniz_wheel

Re: What have been the greatest intellectual achievements? (2017)

#95

Post by Asraelite » Wed, Apr 15, 2026, 11:05 AM UTC

towledev wrote: post #50

Asraelite wrote: post #22

Earlier quoted context omitted.

"nothing" is not the same the same as "zero". "zero apples" means something different to "nothing", but that difference is subtle and difficult to explain, which is what makes the invention of zero such an achievement.

ok, "no apples."

Also not the same. You can't say "the number of apples is no", but you can with "zero".

Re: What have been the greatest intellectual achievements? (2017)

#96

Post by towledev » Thu, Apr 16, 2026, 1:34 AM UTC

Asraelite wrote: post #95

towledev wrote: post #50

Earlier quoted context omitted.

ok, "no apples."

Also not the same. You can't say "the number of apples is no", but you can with "zero".

And that is an all-time great innovation outpacing the Cartesian coordinate system, you say, being able to word a sentence differently

Re: What have been the greatest intellectual achievements? (2017)

#97

Post by towledev » Thu, Apr 16, 2026, 1:37 AM UTC

dtj1123 wrote: post #93

towledev wrote: post #87

Earlier quoted context omitted.

Notably, zero persons have chosen to make the explicit case that zero is more ingenious than the Cartesian coordinate system. :)

Which is a better idea, the brick or the building?

In this case, the building. To give bricks the win over any building ever simply because bricks precede buildings is a little - what’s the word - dumb

Re: What have been the greatest intellectual achievements? (2017)

#98

Post by Asraelite » Thu, Apr 16, 2026, 8:59 AM UTC

towledev wrote: post #96

Asraelite wrote: post #95

Earlier quoted context omitted.

Also not the same. You can't say "the number of apples is no", but you can with "zero".

And that is an all-time great innovation outpacing the Cartesian coordinate system, you say, being able to word a sentence differently

The wording was just an attempt to illustrate the point. There are cases where you can rephrase a sentence with "zero" to get basically the same meaning, but the important thing is that "zero" falls into the same semantic class as other numerals, which other ways of negatively qualifying existence don't.

Put another way, the invention was not literally the word "zero", or anything to do with language per se. It was the idea that you can think about lack of existence in the same was that you think about counting, i.e. treating the idea of there being two apples and the idea of there being zero apples as two examples of the same thing in your mind, instead of treating one as being in some way fundamentally different.

Being raised with a maths education from a young age now, it's easy to see this as obvious, but there was a time in human history when it wasn't.

Also, I wasn't disagreeing with the Cartesian coordinate system being more significant.

Re: What have been the greatest intellectual achievements? (2017)

#99

Post by towledev » Thu, Apr 16, 2026, 2:22 PM UTC

Asraelite wrote: post #98

towledev wrote: post #96

Earlier quoted context omitted.

And that is an all-time great innovation outpacing the Cartesian coordinate system, you say, being able to word a sentence differently

The wording was just an attempt to illustrate the point. There are cases where you can rephrase a sentence with "zero" to get basically the same meaning, but the important thing is that "zero" falls into the same semantic class as other numerals, which other ways of negatively qualifying existence don't. Put another way, the invention was not literally the word "zero", or anything to do with language per se. It was t…

I think ppl really do overrate the "mind shift" needed for zero. That's my honest opinion. I think ppl don't think about it hard enough.

The fact is, zero's usefulness is a bookkeeping device. "There are zero apples" is not better or more useful than "there are no apples." That's not why zero survives. You can wax poetic day and night about what a mind shift "lack of existence is." You're not getting it. You're missing the point. What does that _enable_ that "no apples" does not? That's the measure of its usefulness, right?

It enables positional notation. That's zero's primary gift to the world. It is a necessary bookkeeping device for positional notation. And the measure of positional's usefulness over its predecessor, additive numerals a la the Roman system, is so profoundly great that no argument need be made. No waxing poetic is needed. No "it seems obvious now but back then." It's just indisputable.