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The battle of superiority between sorcerers and wizards goes way back.

The two distinct powerhouses of magic both know that they are tapping into the same magic. However, they do not share the same beliefs about how to use it. Sorcerers use crystal balls, while wizards prefer wooden wands and staves.

It seems that the wizards practice the art of controlling nature and they believed that magic can be broken down into metal, wood, water, fire and earth, the 5 fundamental elements.

Sorcerers, on the other hand, think of magic as permeate all space. They use their crystals like a valve, to control the flow of magic.

Why don't wizards use wand made of crystal, if it is known that they are the best conductor of magic?

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    $\begingroup$ @Penguino's answer is correct, but it doesn't explain why a sensible magician would not use a wooden wand topped with a crystal sphere. A secondary advantage to this is that if you don't have time to prepare a spell, or have temporarily exhausted your magic, it makes a pretty good close-quarters weapon :-) $\endgroup$
    – jamesqf
    Commented Mar 12, 2020 at 4:03
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    $\begingroup$ @jamesqf, the simple answer is that they very often do have a crystal sphere on the staff. There's even a song "A wizard's staff has a knob on the end" (lyrics probably by Nanny Ogg) $\endgroup$
    – Separatrix
    Commented Mar 12, 2020 at 11:08
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    $\begingroup$ @Separatrix Nanny Ogg and Granny Weatherwax both have completely different lyrics for the slightly less popular "This Witch knows where you can shove your staff"... $\endgroup$ Commented Mar 12, 2020 at 13:08
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    $\begingroup$ If you drop a crystal wand it shatters into pieces, Just waving it a round can break many crystals if cut into a long thin shape. It is just not a stable shape for crystals. Power is all well and good but not if you constantly need to replace them. $\endgroup$
    – John
    Commented Mar 12, 2020 at 20:20
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    $\begingroup$ @jamesqf There's no point in having an excellent conductor added to the end of a poor one - the flow has already been bottlenecked. Doesn't matter how wide the "out" channel is, if the "in" channel is too small... $\endgroup$ Commented Mar 13, 2020 at 8:03

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Surely for the simple reason that, if you carried a crystal wand around in your trouser pocket, it would almost certainly break during normal day to day activities. A crystal sphere is fairly strong so long as you don't drop it from a great height. A crystal wand - less so.

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Crystal is too good a conductor of magic.

The wand acts as a resistor, slowing the flow of magic down. This allows the wizards to imprint their will onto it, and control it. A novice wizard has an extremely poor-quality wand, so that the magic tickles through slowly and is easy to control — the problem is, this also means that not much magic is flowing, and the spells are weak.

A stronger wizard has a better quality wand — this allows more magic to flow through it, but it does so faster; it makes the magic harder to control, and requires more skill from the wizard.

As an analogy, imagine a spool of paper running past like a conveyer belt, while you draw runes on it with a paint-brush. This is your spell: the better the conductor your wand is, the faster the paper rushes past, and the faster you need to paint. If your painting isn't good enough, the spell either doesn't work — or it explodes in your hand.

For powerful spells, wizards use wooden staves — being larger, these allow for greater amounts of magic to flow, while still keeping it slow enough to control. (Making the spool of paper wider, instead of faster) Some of them have "reservoirs" at the top, allowing the controlled magic to "pool up" until it is released in a sudden burst through a mounted crystal.

No wizard in history has ever had enough skill to manage more than the simplest of spells with a crystal wand — there just simply isn't enough time to manipulate the magic before it flows out the other end.


A sorcerer, on the other hand, isn't trying to control magic flowing through the crystal ball. Instead, they reach through the crystal ball as a lens or a window, from which to draw upon the vast canvas of magic that surrounds them — like an artist on a cherry-picker spray-painting a large wall. The limiting factor is their own concentration, so a resistive material (small window/reach) would only provide a bottleneck. A crystal ball that allows more flow than you require is no hinderance, once you get it correctly aligned. Higher quality crystals might have more "momentum", and be harder to align though.

This is partly why Sorcerers and Wizards don't get along particularly well (at least, not while casting) - Sorcerers don't like Wizards moving their canvas, and Wizards don't like finding the paper has already been drawn on!

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    $\begingroup$ Sounds a lot like rocket engines for cars. Someone may have made it work once, in a straight line, on flat terrain. But it's not a good idea even under those controlled circumstances. Too much bang for your buck. $\endgroup$
    – Oxy
    Commented Mar 12, 2020 at 12:53
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    $\begingroup$ @Oxy heavy emphasis on "bang". $\endgroup$
    – rcollyer
    Commented Mar 12, 2020 at 13:21
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    $\begingroup$ @StephenS Added something for that $\endgroup$ Commented Mar 12, 2020 at 16:45
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    $\begingroup$ @Oxy Colin Furze would like a word with you. Forget cars, how about jet engines on bikes, go-karts, scooters, not to mention kettles and vacuum cleaners? $\endgroup$ Commented Mar 13, 2020 at 16:33
  • $\begingroup$ @StephenS, MY guess would be that a crystal ball is used only in controlled and and very focused situations. In a desk, in a quiet area where the user can focus all energy on it. $\endgroup$
    – Diesel
    Commented Mar 15, 2020 at 0:16
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Usage cases.

Traditionally, Wizards and Sorcerers do different types of magic. As a result, they need different abilities from their paraphernalia.

Wizards:

enter image description here

  1. Are generally journeymen. As a result, they generally don't feel inclined to carry a 20 pound crystal ball with "Fragile: handle with care" written all over it.

  2. Do smaller spells. While they occasionally need to do something big like blasting Lord Voldemort, they generally only need to do small things like healing and moving boulders. As a result, they don't need the higher magic-conductivity of crystal.

  3. Aren't as well trained. Unlike sorcerers, who train for half a lifetime, Wizards generally pick things up as they go. As a result, they aren't equipped to handle the higher magical bandwidth that comes with using a crystal.

  4. Don't have 3 hours to plan out their spells. To use an idea proposed by @Chronocidal, casting a spell is like writing on a strip of paper as it is being moved past you. While using crystal as a conductor gives you more "space" to work with, it also means that the "paper" is moving much more quickly. Because of this, magicians have to plan out their spells in advance when using crystals, as otherwise the spell will expire while they are still trying to figure out what to "write". Since wizards generally don't have 3 hours to plan out a spell, they instead choose to work around the lower "bandwidth" of a wooden wand.

  5. They need magic right now, not in five hours. Another big difference is how long it takes a wand/crystal to "warm up". While crystal balls are more powerful than wands, they need more magic to do so. Because of this, it takes them a couple hours to build up magic before you can use them. Wands, on the other hand, operate using less mana. This means that while they can't be used for magic-intensive spells, they also don't need to charge in anything but the most low-magic areas.

  6. Don't have \$500,000 available to them. Another thing about crystal balls is that they are expensive; they cost the equivalent of $500,000 to buy. This is because while the crystal itself is a good conductor, the magic it conducts is almost impossible to control unless the crystal is a perfect sphere. As a result, it takes expert craftsmen months to produce a single sphere.


Sorcerers:

enter image description here

  1. Live in one spot. Unlike wizards, sorcerers generally don't move around; they find a high-magic area and set up shop there. As a result, they don't have to carry a highly fragile 20 pound ball across the world with them.

  2. Need to do big spells. Sorcerers usually do big things like building castles or making clone armies. While they occasionally need to do a small spell, they keep around a few wands so that they can do so.

  3. Are very well trained. While wizards pick up magic on the fly, sorcerers spend half a lifetime studying. As a result, they have the requisite experience to handle the high magical "bandwidth" of a crystal.

  4. Can spend years prepping for a single spell. Since they generally operate from highly defensible positions such as the top of a tower, sorcerers can spend as long as necessary to get a spell right. While this means that they aren't very good at doing impromptu magic like wizards, they are able to do really complex spells like, oh, increasing their own lifespan so that they can spend years planning spells.

  5. Have loads of money. Unlike those poor, poverty-stricken wizards, sorcerers usually are very rich; that's why they choose to live in comfort as a sorcerer instead of trekking around in the boondocks.

  6. Need to see what's going on in the world.

enter image description here

One major advantage of crystal balls is that they can also act as Palantíri. This is of immense value to sorcerers, as most newspapers won't deliver to remote towers.

EDIT:

As @MikeCaron pointed out, these roles are reversed in some media.

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    $\begingroup$ This is the kind of answer that deserves bounties. $\endgroup$ Commented Mar 12, 2020 at 21:19
  • $\begingroup$ @Renan Thanks, I appreciate it. $\endgroup$ Commented Mar 12, 2020 at 21:58
  • $\begingroup$ Coming from a largely D&D background, I would argue that the descriptions of your typical wizard and sorcerer are almost entirely backwards. Still, this is a very good answer $\endgroup$
    – Mike Caron
    Commented Mar 13, 2020 at 22:18
  • $\begingroup$ @MikeCaron I come from a Lord of the Rings background. In LotR, wizards (e.g. Gandalf) are travelers, while sorcerers (such as Saruman, Sauron and Melkor) are static. $\endgroup$ Commented Mar 13, 2020 at 22:30
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Sorcerers tap into the flow of magic and try to shift it a bit to get what they want. Wizards control it in a more structured way.

This is like asking, "why do electricians and electrical engineers mostly use copper wires, while computer engineers use semiconductors. Everyone knows copper conducts better than semiconductor, computer engineers must be a bunch of idiots."

Metal, wood, water, fire, and earth are a framework for understanding how particular facets of magic interact with eachother. A well laid out want gives you the option of deflecting the right elements to just where you want them, so they can combine to make a spell. Sorcerers just use a great big conductor because they are gifted at controlling chaos, and adding more energy to the situation means they get to play to that strength.

Perhaps one could also show up with a moon-sun-clay-life wand. That could be another way of viewing the interactions of the magic fields. Tools exist in a framework.

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The TL;DR of the answer: sorcerers are contemplative, wizards are willpower driven.

Sorcerers use the crystal to feel the magic surrounding them, see which entity has to offer what kind of magic and ask a number of those entities for certain combinations and sequences of magic ether releases to achieve a certain effect in a certain place.

To do this, they use the crystal ball:

  1. to reflect the magic landscape around them though the ball
  2. to convey his asking to the magic entities around
  3. to focus the offered magic in producing the effect they want

For all of the above to work, the crystal has to be large, be it only to accurately reflect the magic reality around.

The process is surely going to take more time (even if it will be pretty fast for highly skilled sorcerers, who a "speaking" to the magic world fluently and perceive it in an instant), but are unlikely to produce imbalances in the magic around them and induce decays to to magic depletion.

It is said that high sorcerers can even read the past and intuitively feel the future of a place based on the flow of magic they perceive it there. This is how the legends of divination was created around them, but the temporal dimension of the magic is handled better by other branch of magic... still using crystal ball but even listing the fundamental differences is beyond the scope of this lecture)


By contrast, wizards don't waste time to ask for magic flows to be offered, they demand it and, when they feel it's needed, they forcefully appropriate it by the use of spells. They are living here and now, reacting swiftly and taking fast (and not rarely hasty) decisions.

At high level of proficiency, wizards won't affect the balance of magic in the surroundings by requisitioning what they need - at least not when they can avoid it. They don't do it from an empathic or feeling based ethics, their approach is strictly pragmatic - those that did that in the past didn't last long in confrontations, no matter how strongly willed one is, one can't take anything from a place they depleted earlier.

Now, sensu stricto, it is improper to say the wizards do not use crystals to control the flow of magic. After all, not every material is appropriate to make a magical wand from. At microscopic level, no matter the wand overall material, there are strands of crystal that channel the flow of magic. The already known requirement of a certain degree of fitness between a wizard and his wand has explanation in the way the configuration of these strands (and the interplay of the strands with the embedding matrix) feel for the prospective owner. Where for most of the other wizards feel the constraints of the matrix and bending or torsion of the crystal strands as impeding the magic flow, the prospective owner feels opportunities of flow control and modulation of the wave of this flow.

the ability of a wizard to take control on the wand of a wizard foe they defeated in a fight stems from the fact they felt and internalized how the opponent used it - it is a necessary condition to withstand and repel the spells and the burst of magic shaped and directed as attack vectors.

S/he won't be able to have the same proficiency using the captured wand as when using their own, but still the level of control over the captured wand is 1 or 2 levels of magnitude better then any other still-alive wizards

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Resonance versus Impedance, Grapes and Whips

The crystal ball has a high magical index of refraction and acts as a resonating chamber (like the grapes making plasma in a microwave).

While wood has a lower magical index of refraction, and the tapered end is even lower. It serves as a bridge, matching the index of the spell caster on one side and the vacuum on the other, much like whips do with the large end tapering to the small end. (This is called impedance matching.)

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Too stubborn to admit they're wrong

If the difference between wizards and sorcerers boils down to belief, it could very well be that for wizards to admit that crystal balls are superior would be admitting that they're wrong and sorcerers are right and thus they're too stubborn to admit otherwise to the point that they're subconsciously deluding themselves to the contrary. A profound example of confirmation bias.

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Wizards are versatile, sorcerers are powerful

Because they come from a living tree with affinity to multiple elements (wood, earth, water, air?), wooden wands and staves act as an interface between these elements and are much better suited to controlling and switching between different types of magics.

On the other hand, crystal allows raw magic to flow through it much more effectively, but is less adaptable in the shape that magic takes when used in a spell.

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Material Properties

The Sorcerer uses his crystal ball to draw magic in, then siphons it off to cast himself. Essentially a Crystal ball is a magical capacitor.
A more subtle use is that as magic is drawn to the ball, it retains some information of where it came from (at least until it's absorbed) and a skillful wielder can use the crystal ball to scry the history of an area, view events, see through walls and so on, all based on the magical afterimages being drawn into his crystal ball.

The caveat is that changing the shape of the crystal doesn't meaningfully affect its behaviour, so a crystal wand would absorb magic in the same way as a crystal ball.
With more complex topology it makes it harder to read the "afterimages" being brought with it. So a wand is purely useful for its magical capacitor behaviour, not for anything more subtle.
It doesn't act as a channel for magic, unlike wood.

Wood does not absorb magic, it purely channels it along its length for accuracy.

A magic-user therefore uses Crystals to draw magic to them, and wooden wands or staves to channel it into what they want to do.

Wizards practice a kind of magical leverage, using magical items and ingredients as fuel for their spells. draining the magic from an object using smaller crystals and shunting it elsewhere in a new form.

Sorcerers meanwhile prefer to draw magic to them with crystal balls and cast directly from that.

The wizard approach works well for preparing complex/precise spells that mustn't receive more power than required, while the sorcerer's approach lends itself to a more rough-and-ready style of magic, but relies on there being magic to use.

A Sorcerer therefore needs to find ley-lines or places of high background-magic to perform more powerful spells, while a wizard generally needs to find artefacts of power to accomplish the same.

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Because crystal doesn't react well to being shaken about

You can hold a wand and wave it around, point it at people, magic still comes out fine. If you're using crystal though, it needs to be placed on a flat, rigid surface and kept still, otherwise the magic comes out all wobbly and smudged.

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Magical Optics!

It isn't just the material of the Crystal balls that enables them to be a conduit for magic.

It is also their shape. Their optics.

Magic is a discrete "thing" of the universe. It flows around space, and it is carried along more or less like photons.

Just like photons, it can interact with some materials for different results - it may be absorbed, redirected, etc. The exact specifics of the rules "Magicons" obey don't need to follow the same as the rules of the photons, but you can use them as a starting point to determine how magic and different materials interact.

On the specific case of the crystal balls, they are an unique type of object that mix two important properties - the ability to conduct magic, and the ability to redirect magic - into a single, conveniently shaped object that is easy to use. A crystal wand wouldn't have the same optics, so it wouldn't be as useful for casting magic.

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TL;DR: It is the best conductor of magic, but wizards need more than that to ply their magic.

Longer Answer:

Disclaimer: I am going to proceed on the D&D-style premise that a wizard studies magic while it is innate to a sorcerer. All other factors will be as even as needed.

The question states that crystals are the best conductors of magic and is known. However, also according to the question wizards eschew it in favour of wooden implements. To me, this indicates that it was a conscious choice to venture away from crystals for their main spellcasting.

With wizards believing that magic can be broken down into base elements, their training would lead them to create a tool to assist them with that. Not only does it need to channel magic, but it also needs to do all the other fiddly things that they want to do as well. Crystal might be the best at channeling pure magic, but it is inferior in other metrics.

Other materials like bone, stone, and metals were tested for their uses. Each material has its advantages and drawbacks when it comes to their method of spellcasting. In the end, wood was chosen for being average in performance across the board. It has the ability to be shaped into something more conducive to the wizard as well as being adaptable to many situations. It is also easier to cultivate suitable trees to keep the traditions alive compared to using the bones of wizards past or sacred metals.

In contrast to this, the spells of a sorcerer are innate and known as opposed to gained through study. They do not require the same fine manipulation of magic to warrant needing a wand of wood or bone. They need to tap into the power and harmonize it with themselves to make magic. Crystal provides a conduit to channel more power faster. The orb shape is easier to made than others as well as being potentially harder to break than a crystal stick ... er wand.

Since they only need the power around them, a crystal implement is perfect for their needs. A valve to control the power so it does not control them.

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Sorcerers are more contemplative. They use crystal balls in order to scry. To gather information and carefully make plans. Wizards are more active and direct. Their wands provide more raw power.

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Cristal balls:

  • Can store and release a large amount of magic stored.
  • Sorcerer have problems draining magic from nature, having a crystall ball allow them to have a bigger reserve of magic.
  • Precious jewells are better but usually much more expencive and smaller, a diamond the size of a humam fist would be thousands times better than a comon crystal ball, but they would be extremally rarer.
  • Some jewells like rubys will give elements to the magic stored making fire magic less consuming and more powerfull for example.
  • Some more powerfull and better crafted crystal ball can cast spells by simple shouting the spell name or reacting automatically at enemies atacks for exemple.
  • While not admiting the goodnes of a wand, some sorceres have wood structures around the crystall ball that improve the object habilities.

Wands:

  • Can be made of various types of woods, relativaly cheaper, but some types of rarer woods can be priceless material for a wand.
  • Due to the connection with nature, wizards have great hability draining magic from the enviroment, the greater the wizard greater is the amount of magic they can borrow, needing better wands even stafs to handle the amount.
  • Wands can come in various forms, usually they are magical wands, canes and staffs.
  • Some wizards have jewells embed in theyr wands to strengthen some types of magic, but they never admit the importance of it.
  • Wands are fasters to pull and easier to conceal, staffs can be used as blunt weapons and walking suports.
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    $\begingroup$ What does "armazene" mean? $\endgroup$ Commented Mar 13, 2020 at 21:58
  • $\begingroup$ Sorry. I meant 'store' I'm non native speaker, sometimes it gets confusing. $\endgroup$ Commented Mar 16, 2020 at 11:32
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Critical Mass

The crystal needs to achieve a certain critical mass (like uranium or plutonium) to function properly.

The most efficient shape for achieving a critical mass is a sphere, and that sphere needs to be a certain size or greater to function at all.


Density

That particular crystal is so dense that a useful amount of it is difficult to carry. A 50 pound wand isn't very practical... The weight of a crystal ball sitting atop a stone slab of a table on the other hand, is largely irrelevant. None too mobile though.

OTOH, a stone golem with a relatively small crystal ball inside it's torso could make for a potent magical siege weapon.

And perhaps it is this density that is the key to its special properties. "The atoms are closer together" or some such.


Position Locked

In order to function, crystal must be bound to a particular place. Moving the crystal breaks that binding, rendering it inert.

The binding process is nontrivial. Perhaps it is a ritual, or requires more energy than a single wizard or sorcerer has access to. Using up all your energy in the field isn't practical.

Variant B:

The longer a crystal is in a particular spot, the more powerful it becomes (perhaps it approaches some limit or other based on the size of the orb). Maybe it's "adapting to the local mana flows" or something. A crystal of any shape you walk around with is all but useless, but one that's been in the same spot for decades or centuries could bend reality into a pretzel at the sorcerer's whim.

At this point, a wizard's "win condition" is to force that crystal ball to move. Divert a river, trigger an earthquake, open a sinkhole under their position, "disturb the local flows of mana", etc.

And a sorcerer just needs to get a wizard close enough to their orb to overwhelm them.

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