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Comment by adrian_b | Hacker News Reader

The reason why which charge is named positive and which is named negative does not matter is because in all the equations that relate electric charge with other measurable physical quantities we never have an electric charge alone, but we always have the product of two electric charges.

The value of the product of two electric charges is invariant to the convention chosen for the sign of the electric charge.

Numbers and numeric quantities are actually a real thing that exists in the world. They do not exist only in our minds (and in the minds of many other animals who are also able to count until some small number). And so does the concept of negation, which clearly is a property of the world, independent of humans or animals.

For other physical quantities, the sign of a quantity is not arbitrary, like for the electric charge, because those are used in expressions that are not invariant to sign changes.

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It didn't matter in Franklin's time, but it came to matter later, due to the discovery or invention of devices in which it matters which charge carrier is moving.

For example, in naming the parts of a NPN bipolar junction transistor, the negatively connected terminal is the "emitter", and the positive one the "collector". The base-emitter diode arrow points toward the emitter.

So? That things "normally" should move positive to negative or vice versa is also a convention.

It helps me visually when looking at a circuit diagram if I can think about the current flowing "down", like most rivers do in the Northern Hemisphere. It's just a vague association in my mind, but it is based in physical reality.

what do you mean by most rivers flowing down in the northern hemisphere?

That convention is the result of identifying current flow as being the movement of that which we identified as positive charge.

It's not a convention that like charges repel.

If we agree that current is the flow of positive charge, then it has to go away from positive, toward negative.

Using positive quantities for current and charge is a good thing; we aren't constantly dealing with negative numbers to measure common situations like how much current is flowing through a wire.

Negation, being a concept, exists only in the mind. Same with "things". A thing is a noun; a part of speech. The "real world" is undifferentiated quanta.

Put simply, "the map is not the territory"

Or, as Monty Python has rightly pointed out, "it's only a model."

It would be a bad convention for a map to use valleys to represent mountains.

If that just a nominal change, such as just switching the color convention it uses for montains vs valleys, then it would be fine.

And that's the case with positive/negative.

While in the mathematics of the later part of the 19th century and of the 20th century there have been developed many theories with very abstract concepts for which it may be claimed that those concepts have been invented in the minds of some mathematicians without a direct correspondence with the world experienced by them, such a claim would be false about almost any concept in the mathematics developed until the 19th century, because almost all older mathematical concepts are just abstractions of properties of the physical world.

For instance, what happens when you connect the two electrodes of a battery to the pins of a semiconductor diode will differ depending on whether you negate the battery or not (i.e. you revert or not its connections). What happens with a ball (or with a thrown stone) will differ depending on whether its velocity is positive or negative, and so on.

Additions and subtractions of physical quantities, therefore also negation, happen in the physical world regardless of the presence of sentient beings.

Humans can recognize such properties of the world and give them names and integrate them in coherent mathematical models, but the base concepts are not inventions, they are the result of empirical observations.

Careful!

> What happens with a ball (or with a thrown stone) will differ depending on whether its velocity is positive or negative, and so on.

The velocity of a ball is a vector. Using a positive or negative number to describe it is a manner of convention. When you say that you threw a ball with “positive 7 mph” velocity, you need to explain what you mean.

One might argue that there really is a ball and that it has a velocity and that the velocity really is an element in a vector field originating [0] at the center of mass of the ball. Debating to what extent this is fundamentally true or is just a useful concept that people came up with would be interesting.

[0] In general relativity, space is not Euclidean (nor is it a flat Minkowski space), and velocity vectors are only really meaningful in association with a point in spacetime. You can read all about tangent bundles in Wikipedia :)

Ceci n'est pas une pipe

I have an hard time coming to terms with this platonic view of the mind, as if our minds where some kind of extradimensional aliens playing with this sandbox of "undifferentiated quanta" sometime called reality.

I understand how it make sense saying that the concept of spedrunning is completely absent in Ocarina Of Time and only exists in the player playing the game, but I do not see how this would be a good philosophy to apply to ourselves.

I confess that I have a particular aversion to this specific philosophy/POV because I feel like it is riding on the respectability and "coolness" of science to sound more serious while being just another metaphysics without (IMHO) any* particularly good qualities.

* Ok, I admit that it has at least a good quality: it is a good example of a non-religious metaphysics to give to people that cannot imagine a non-religious metaphysics.

Philosophies are tools for reasoning. I don't literally go through my life thinking "oh here's an undifferentiated quanta, time to apply some nouns to it." But if I want to adopt a scientific mindset it's beneficial to think in terms of the physical experience versus my mental model of it because I can write my mental model down, whereas I can't write physical experiences or undifferentiated quanta down. That's what makes them quanta.

We have tons of sayings for this like "the map is not the territory," "wherever you go that's where you are."

Only according to some epistemologies.

There is a way in that it matters: in a vacuum tube you can have cathodic rays but (pragmatically) not anodic rays.

IIRC a Veritasium video claims that these where essentially discovered by mistake in lightbulbs, so I suspect that Franklin would have had a hard time finding them...

But a cathode is that terminal of the device where positive current escapes!

It's only a "cathode ray" because it's reversed inside the tube: the terminal where positive current comes out of the device is where the negative current emanates internally to go to the other terminal.

An electron beam shooting out of a device is an anode ray.

I always mix them up... :(

If we make an oscillating circuit by hooking up an inductor and capacitor and set it in motion, the devices are constantly switching their terminal designations between anode and cathode with each zero crossing. The terms are completely useless, except when talking about vacuum tube circuits and such.

Numbers do not exist in the world. Umbers exist outside the world.

I do not know if this is a joke about shadows that I did not get, or just a typo, but numbers exist in the world.

The world is composed of things. The things are grouped in sets. Numbers are equivalence classes of sets.

The set of the medium-sized planets of the Solar System is equivalent in number with the set of the big planets of the Solar System and also equivalent in number with the set of the big satellites of Jupiter (i.e. 4).

Such equivalences between sets of things exist regardless if there are any sentient beings that recognize those equivalences and there are circumstances when for instance the evolution in time of some sets of things is determined or influenced by the relationship between the numbers of things that compose each set.

> The things are grouped in sets.

By who?

Our current universe

Even before the appearance of life, the things group in sets spontaneously, due to the interplay between attractive and repulsive forces and the positive feedbacks that appear in certain conditions.

The world is not made of a homogeneous substance, but there are various kinds of groupings at various levels, nucleons and electrons group in atoms, atoms group in molecules, molecules group in pebbles, stars group in galaxies and so on.

Us?

If one take the position tha minds are not part of the "real world" then you end up defining "reality" by some random model.

It is just as absurd as saying that the only thing that exists is my own perception and you are "just" a ghost my mind is "thinking into existence".

It sounds less crazy only because we are used to reductionism being generally more useful, but what is the usefullness of concepts like reality and existence when defined to mean that we and our minds (the only thing we perceive) are not "real" or do not really "exist"?

By themselves already.

E.g. there are 10 rock formations in this part of the desert, and 2 rocks in the other side.

There is a clustering (set) of 10 vs 2 even if we aren't there to measure them and group them.

As are other sets co-existing (like the whole desert has 12 rock formations, while some other has only sand).

Numb and Number

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