OpenLLM-France/wikimedia huggingface dataset:
# Computer Programming/Physics/Position of an accelerating body function

Wikisource:Source code
The position of an accelerating body can be described by a mathematical function $\mathbf {s} (t)$. The generalized function can be attained by using the Taylor series
    $\mathbf {s} (t+t_{0})=\sum {\frac {t^{n}}{n!}}\mathbf {s} ^{(n)}(t_{0})$,
where $\mathbf {s} ^{(n)}$ is the $nth$ derivative of $\mathbf {s}$:
   * $\mathbf {s} ^{(0)}={\frac {d^{0}\mathbf {s} }{dt^{0}}}=\mathbf {s}$
   * $\mathbf {s} ^{(1)}={\frac {d^{1}\mathbf {s} }{dt^{1}}}=\mathbf {v}$
   * $\mathbf {s} ^{(2)}={\frac {d^{2}\mathbf {s} }{dt^{2}}}=\mathbf {a}$
   * etc.
The accuracy of this function depends on the number of terms used as ${\frac {1}{n!}}$ decreases rapidly. Additionally, the time $t$ can be synchronized such that $t_{0}=0$ (Maclaurin series).
Note that for a constant acceleration most of the terms become zero and we're left with
    $s(t)={\frac {1}{0!}}\mathbf {s} _{0}+{\frac {t}{1!}}\mathbf {s} _{0}^{(1)}+{\frac {t^{2}}{2!}}\mathbf {s} _{0}^{(2)}$
or
    $\mathbf {s} (t)=\mathbf {s} _{0}+\mathbf {v} _{0}t+{\frac {1}{2}}\mathbf {a} t^{2}$

## Justification for Using the Taylor Series

The Taylor series can be derived by systematically selecting which of our variables is a constant and then extrapolating that to the infinite limit.
* Constant Position
       $s(t)=s_{0}$
       or
       $s(t)={\frac {t^{0}}{0!}}s^{(0)}(t_{0}=0)$
* Constant Velocity
       $v(t)=v_{0}$
       $s(t)=\int vdt=\int v_{0}dt$
       $s(t)=v_{0}t+s_{0}$
       or
       $s(t)={\frac {t^{0}}{0!}}s^{(0)}(t_{0}=0)+{\frac {t^{1}}{1!}}s^{(1)}(t_{0}=0)$
* Constant Acceleration
       $a(t)=a_{0}$
       $v(t)=\int adt=\int a_{0}dt$
       $v(t)=a_{0}t+v_{0}$
       $s(t)=\int vdt=\int (a_{0}t+v_{0})dt$
       $s(t)={\frac {1}{2}}a_{0}t^{2}+v_{0}t+s_{0}$
       or
       $s(t)={\frac {t^{0}}{0!}}s^{(0)}(t_{0}=0)+{\frac {t^{1}}{1!}}s^{(1)}(t_{0}=0)+{\frac {t^{2}}{2!}}s^{(2)}(t_{0}=0)$
* Constant Rate of Change of Acceleration
       $a^{(1)}(t)=a_{0}^{(1)}$
       $a(t)=\int a^{(1)}dt=\int a_{0}^{(1)}dt$
       $a(t)=a_{0}^{(1)}t+a_{0}$
       $v(t)=\int adt=\int (a_{0}^{(1)}t+a_{0})dt$
       $v(t)={\frac {1}{2}}a_{0}^{(1)}t^{2}+a_{0}t+v_{0}$
       $s(t)=\int vdt=\int ({\frac {1}{2}}a_{0}^{(1)}t^{2}+a_{0}t+v_{0})dt$
       $s(t)={\frac {1}{6}}a_{0}^{(1)}t^{3}+{\frac {1}{2}}a_{0}t^{2}+v_{0}t+s_{0}$
       or
       $s(t)={\frac {t^{0}}{0!}}s^{(0)}(t_{0}=0)+{\frac {t^{1}}{1!}}s^{(1)}(t_{0}=0)+{\frac {t^{2}}{2!}}s^{(2)}(t_{0}=0)+{\frac {t^{3}}{3!}}s^{(3)}(t_{0}=0)$
* etc.
# Economic Sophisms/159

<pagequality level="3" user="Zoeannl" />style="background: #ececec; text-align: left; padding-left: 0.5em; font-weight: bold;" class="table-rh"Template:Hwe?" His first impulse is to answer "No," and the Odier Committee proudly welcome his response.
However, we must go a little deeper into the matter. Unquestionably, foreign competition—nay, competition in general—is always troublesome; and if one branch of trade alone could get quit of it, that branch of trade would for some time profit largely.
But protection is not an isolated favour; it is a system. If, to the profit of the agriculturist, protection tends to create a scarcity of corn and of meat, it tends likewise to create, to the profit of other industries, a scarcity of iron, of cloth, of fuel, tools, etc.,—a scarcity, in short, of everything.
Now, if a scarcity of corn tends to enhance its price through a diminution of supply, the scarcity of all other commodities for which corn is exchanged tends to reduce the price of corn by a diminution of demand, so that it is not at all certain that ultimately corn will be a penny dearer than it would have been under a system of free trade. There is nothing certain in the whole process but this—that as there is upon the whole less of every commodity in the country, each man will be less plentifully provided with everything he has occasion to buy.
The agriculturist should ask himself whether it would not be more for his interest that a certain quantity of corn and cattle should be imported from abroad, and that he should at the same time find himself surrounded by a population in easy circumstances, able and willing to consume and pay for all sorts of agricultural produce.
Suppose a department in which the people are clothed in rags, fed upon chesnuts, and lodged in hovels. How can agriculture flourish in such a locality? What can the soil be made to produce with a well-founded expectation of fair remuneration? Meat? The people do not eat it. Milk? They must content themselves with water. Butter? It is regarded as a luxury. Wool? The use of it is dispensed with as much as possible. Does any one imagine that all the ordinary objects of consumption can thus be put beyond the reach of the masses, without tending to lower prices as much as protection is tending to raise them?
What has been said of the agriculturist holds equally true
# Economic Sophisms/156

<pagequality level="3" user="Zoeannl" />style="background: #ececec; text-align: left; padding-left: 0.5em; font-weight: bold;" class="table-rh"boast so much." To which the reply was, "It is liberty which has induced the dearness which you find so useful"
At this rate, would it not be amusing to see cheapness become the watch-word of the Rue Hauteville, and dearness the watchword of the Rue Choiseul?
Evidently there is in all this a misconception, an illusion, which it is necessary to clear up; and this is what I shall now endeavour to do.
Put the case of two isolated nations, each composed of a million of inhabitants. Grant that, cœteris paribus, the one possesses double the quantity of everything,—corn, meat, iron, furniture, fuel, books, clothing, etc.,—which the other possesses. It will be granted that the one is twice as rich as the other.
And yet there is no reason to affirm that a difference in actual money prices exists in the two countries. Nominal prices may perhaps be higher in the richer country. It may be that in the United States everything is nominally dearer than in Poland, and that the population of the former country should, nevertheless, be better provided with all that they need; whence we infer that it is not the nominal price of products, but their comparative abundance, which constitutes wealth. When, then, we desire to pronounce an opinion on the comparative merits of restriction and free-trade, we should not inquire which of the two systems engenders dearness or cheapness, but which of the two brings abundance or scarcity.
For, observe this, that products being exchanged for each other, a relative scarcity of all, and a relative abundance of all, leave the nominal prices of commodities in general at the same point; but this cannot be affirmed of the relative condition of the inhabitants of the two countries.
Let us dip a little deeper still into this subject.
* ↑ Recently, M. Duchâtel, who had formerly advocated free trade, with a view to low prices, said to the Chamber: It would not be difficult for me to prove that protection leads to cheapness.
* ↑ The expression, prix absolus (absolute prices), which the author employs here and in chap. xi. of the First Series (ante), is not, I think, used by English economists, nd from the context in both instances I take it to mean actual money prices; or what Adam Smith terms nominal prices.,—TRANSLATOR.
# Economic Sophisms/153

<pagequality level="3" user="Zoeannl" />style="background: #ececec; text-align: left; padding-left: 0.5em; font-weight: bold;" class="table-rh"Here is another report:—
| EFFECTS OF PROTECTION.—REPORT OF THE BLACKSMITHS. |
| Inconveniences. | Advantages, |
| 1st, The policy of protection imposes a tax upon us every time we eat, drink, or warm or clothe ourselves, and this tax does not go to the treasury. | None. |
| 2d, It imposes a like tax upon all our fellow-citizens who are not of our trade, and they, being so much the poorer, have recourse to cheap substitutes for our work, which deprives us of the employment we should otherwise have had. | None. |
| 3d, It keeps up iron at so high a price, that it is not employed in the country for ploughs, grates, gates, balconies, etc.; and our trade, which might furnish employment to so many other people who are in want of it, no longer furnishes employment to ourselves. | None. |
| 4th, The revenue which the treasury fails to obtain from commodities which are not imported, is levied upon the salt we use, postages, etc | None. |
All the other reports (with which it is unnecessary to trouble the reader) are to the same tune. Gardeners, carpenters, shoemakers, clogmakers, boatmen, millers, all give vent to the same complaints.
I regret that there are no agricultural labourers in our association. Their report would assuredly have been very instructive.
But, alas! in our country of the Landes, the poor labourers, protected though they be, have not the means of joining an association, and, having insured their cattle, they find they cannot themselves become members of a friendly society. The boon of protection does not hinder them from being the parias of our social order. What shall I say of the vine-dressers?
What I remark, especially, is the good sense displayed by our villagers in perceiving not only the direct injury which the policy of protection does them, but the indirect injury, which, although in the first instance affecting their customers, falls back, par ricochet, upon themselves.
This is what the economists of the Moniteur Industriel do not appear to understand.
And perhaps those men whose eyes a dash of protection has fascinated, especially our agriculturists, would be willing to give it up, if they were enabled to see this side of the question. In that case they might perhaps say to themselves, "Better far to be self-supported in the midst of a set of customers in easy circumstances, than to be protected in the midst of an impoverished clientèle.
For to desire to enrich by turns each separate branch of industry by creating a void round each in succession, is as vain an attempt as it would be for a man to try to leap over his own shadow.
# Economic Sophisms/157

<pagequality level="3" user="Zoeannl" />style="background: #ececec; text-align: left; padding-left: 0.5em; font-weight: bold;" class="table-rh"When we see an increase and a reduction of duties produce effects so different from what we had expected, depreciation often following taxation, and enhancement following free trade, it becomes the imperative duty of political economy to seek an explanation of phenomena so much opposed to received ideas; for it is needless to say that a science, if it is worthy of the name, is nothing else than a faithful statement and a sound explanation of facts.
Now the phenomenon we are here examining is explained very satisfactorily by a circumstance of which we must never lose sight.
Dearness is due to two causes, and not to one only.
The same thing holds of cheapness.
It is one of the least disputed points in political economy that price is determined by the relative state of supply and demand.
There are then two terms which affect price—supply and demand. These terms are essentially variable. They may be combined in the same direction, in contrary directions, and in infinitely varied proportions. Hence the combinations of which price is the result are inexhaustible.
High price may be the result, either of diminished supply, or of increased demand.
Low price may be the result of increased supply, or of diminished demand.
Hence there are two kinds of dearness, and two kinds of cheapness.
There is a dearness of an injurious kind, that which proceeds from a diminution of supply, for that implies scarcity, privation (such as has been felt this year from the scarcity of corn); and there is a dearness of a beneficial kind, that which results from an increase of demand, for the latter presupposes the development of general wealth.
In the same way, there is a cheapness which is desirable, that which has its source in abundance ; and an injurious cheapness, that has for its cause the failure of demand, and the impoverishment of consumers.
Now, be pleased to remark this ; that restriction tends to
induce, at the same time, both the injurious cause of dearness,
# Economic Sophisms/158

<pagequality level="3" user="Zoeannl" />style="background: #ececec; text-align: left; padding-left: 0.5em; font-weight: bold;" class="table-rh"and the injurious cause of cheapness: injurious deamess, by diminishing the supply, for this is the avowed object of restriction; and injurious cheapness, by diminishing also the demand; seeing that it gives a false direction to labour and capital, and fetters consumers with taxes and trammels.
So that, as regards price, these two tendencies neutralize each other; and this is the reason why the restrictive system, restraining, as it does, demand and supply at one and the same time, does not in the long run realize even that dearness which is its object.
But, as regards the condition of the population, these causes do not at all neutralize each other; on the contrary, they concur in making it worse.
The effect of freedom of trade is exactly the opposite. In its general result, it may be that it does not realize the cheapness it promises; for it has two tendencies, one towards desirable cheapness through the extension of supply, or abundance; the other towards appreciable dearness by the development of demand, or general wealth. These two tendencies neutralize each other in what concerns nominal price, but they concur in what regards the material prosperity of the population.
In short, under the restrictive system, in as far as it is operative, men recede towards a state of things, in which both demand and supply are enfeebled. Under a system of freedom, they progress towards a state of things in which both are developed simultaneously, and without necessarily affecting nominal prices. Such prices form no good criterion of wealth. They may remain the same whilst society is falling into a state of the most abject poverty, or whilst it is advancing towards a state of the greatest prosperity.
We shall now, in a few words, show the practical application of this doctrine.
A cultivator of the south of France believes himself to be very rich, because he is protected by duties from external competition. He may be as poor as Job; but he nevertheless imagines that sooner or later he will get rich by protection. In these circumstances, if we ask him the question which was put by the Odier Committee in these words,—
"Do you desire—yes or no—to be subject to foreign Template:Hws
# Economic Sophisms/155

<pagequality level="3" user="Zoeannl" />style="background: #ececec; text-align: left; padding-left: 0.5em; font-weight: bold;" class="table-rh"'the bitter enemies of laissez faire. At all hazards they want the law to interfere, without knowing or caring in what direction. And yet it lies with those who desire to create by legal intervention an artificial dearness or an unnatural cheapness, to explain the grounds of their preference. The onus probandi rests upon them exclusively. Liberty is always esteemed good, till the contrary is proved; and to allow prices to settle and adjust themselves naturally, is liberty.
But the parties to this dispute have changed positions. The advocates of dearness have secured the triumph of their system, and it lies with the defenders of natural prices to prove the goodness of their cause. On both sides, the argument turns on two words; and it is therefore very essential to ascertain what these two words really mean.
But we must first of all notice a series of facts which are fitted to disconcert the champions of both camps.
To engender dearness, the restrictionists have obtained protective duties, and a cheapness, which is to them inexplicable, has come to deceive their hopes.
To create cheapness, the free-traders have occasionally succeeded in securing liberty, and, to their astonishment, an elevation of prices has been the consequence.
For example, in France, in order to favour agriculture, a duty of 22 per cent, has been imposed on foreign wool, and it has turned out that French wool has been sold at a lower price after the measure than before it.
In England, to satisfy the consumer, they lowered, and ultimately removed, the duty on foreign wool; and it has come to pass that in that country the price of wool is higher than ever.
And these are not isolated facts; for the price of wool is governed by precisely the same laws which govern the price of everything else. The same result is produced in all analogous cases. Contrary to expectation, protection has, to some extent, brought about a fall, and competition, to some extent, a rise of prices.
When the confusion of ideas thence arising had reached its height, the protectionists began saying to their adversaries, "It
is our system which brings about the cheapness of which you
# Economic Sophisms/154

<pagequality level="3" user="Zoeannl" />style="background: #ececec; text-align: left; padding-left: 0.5em; font-weight: bold;" class="table-rh"
I THINK it necessary to submit to the reader some theoretical remarks on the illusions to which the words dearness and cheapness give rise. At first sight, these remarks may, I feel, be regarded as subtle, but the question is not whether they are subtle or the reverse, but whether they are true. Now, I not only believe them to be perfectly true, but to be well fitted to suggest matter of reflection to men (of whom there are not a few) who have sincere faith in the efficacy of a protectionist policy.
The advocates of Liberty and the defenders of Restriction are both obliged to employ the expressions, dearness, cheapness. The former declare themselves in favour of cheapness with a view to the interest of the consumer; the latter pronounce in favour of dearness, having regard especially to the interest of the producer. Others content themselves with saying, The producer and consumer are one and the same person; which leaves undecided the question whether the law should promote cheapness or dearness.
In the midst of this conflict, it would seem that the law has only one course to follow, and that is to allow prices to settle and adjust themselves naturally. But then we are attacked by
# Economic Sophisms/16

<pagequality level="4" user="Zoeannl" />style="background: #ececec; text-align: left; padding-left: 0.5em; font-weight: bold;" class="table-rh"Articles of convenience, 10 per cent.
Articlies of luxury, 15 to 20 per cent.
These distinctions, I am aware, belong to an order of ideas which are quite foreign to Political Economy strictly so called, and I am far from thinking them as just and useful as they are commonly supposed to be. But this subject does not fall within the compass of my present design.
# Economic Sophisms/160

<pagequality level="3" user="Zoeannl" />style="background: #ececec; text-align: left; padding-left: 0.5em; font-weight: bold;" class="table-rh"of the manufacturer. Our manufacturers of cloth assure us that external competition will lower prices by increasing the supply. Granted; but will not these prices be again raised by an increased demand? Is the consumption of cloth a fixed and invariable quantity? Has every man as much of it as he would wish to have? And if general wealth is advanced and developed by the abolition of all these taxes and restrictions, will the first use to which this emancipation is turned by the population not be to dress better?
The question,—the constantly-recurring question,—then, is not to find out whether protection is favourable to any one special branch of industry, but whether, when everything is weighed, balanced, and taken into account, restriction is, in its own nature, more productive than liberty.
Now, no one will venture to maintain this. On the contrary, we are perpetually met with the admission, "You are right in principle."
If it be so, if restriction confers no benefit on individual branches of industry without doing a greater amount of injury to general wealth, we are forced to conclude that actual money prices, considered by themselves, only express a relation between each special branch of industry and industry in general, between supply and demand; and that, on this account, a remunerative price, which is the professed object of protection, is rather injured than favoured by the system.
The article which we have published under the title of Dearness, Cheapness, has brought us several letters. We give them, along with our replies:—
Template:Fs90/s MR EDITOR,—You upset all our ideas. I endeavoured to aid the cause of free trade, and found it necessary to urge the consideration of cheapness, I went about everywhere, saying, "When freedom of trade is accorded, bread, meat, cloth, linen, iron, fuel, will go on falling in price." This displeased those who sell, but gave great pleasure to those who buy these commodities. And now you throw out doubts as to whether free trade willTemplate:Fs90/e
# Economic Sophisms/152

<pagequality level="3" user="Zoeannl" />style="background: #ececec; text-align: left; padding-left: 0.5em; font-weight: bold;" class="table-rh"dyers, blacksmiths, innkeepers, grocers, etc., etc.,—and who, in my village, have founded friendly society.
I have transformed this friendly society, at my own hand, into a Lower Council of Labour, and instituted an inquiry which will be found of great importance, although it is not crammed with figures, or inflated to the bulk of a quarto volume, printed at the expense of the State.
My object was to interrogate these plain, simple people as to the manner in which they are, or believe themselves to be, affected by the policy of protection. The president pointed out that this would be infringing to some extent on the fundamental conditions of the Association. For in France, this land of liberty, people who associate give up their right to talk politics—in other words, their right to discuss their common interests. However, after some hesitation, he agreed to include the question in the order of the day.
They divided the assembly into as many committees as there were groups of distinct trades, and delivered to each committee a schedule to be filled up after fifteen days' deliberation.
On the day fixed, the worthy president (we adopt the official style) took the chair, and there were laid upon the table (still the official style) fifteen reports, which he read in succession. The first which was taken into consideration was that of the tailors. Here is an exact and literal copy of it:—
EFFECTS OF PROTECTION.—REPORT OF THE TAILORS. :
| Inconveniences. | Advantages, |
| 1st, In consequence of the policy of protection, we pay dearer for bread, meat, sugar, firewood, thread, needles, etc., which is equivalent in our case to a considerable reduction of wages. | None. |
| 2d, In consequence of the policy of protection, our customers also pay dearer for everything, and this leaves them less to spend upon clothing; whence it follows that we have less employment, and, consequently, smaller returns. | Note.—After all our inquiries, deliberations, and discussions, we have been quite unable to discover that in any respect whatever the policy of protection has been of advantage to our trade. |
| 3d. In consequence of the policy of protection, the stuffs which we make up are dear, and people on that account wear their clothes longer, or dispense with part of them. This, again, is equivalent to a diminution of employment, and forces us to offer our services at a lower rate of remuneration. | Note.—After all our inquiries, deliberations, and discussions, we have been quite unable to discover that in any respect whatever the policy of protection has been of advantage to our trade. |
# Castle of the Winds

This book was created to document the 1989 game Castle of the Winds.

## Contents

* Introduction
* Obtaining the Game
* System Requirements
* Gameplay
** Interface & Controls
** Battle Mechanics
*** Monsters
** Items and the Inventory System
** Magic
** Character Attributes
** Story and Locations
* Strategy
* Cheats and Exploits
* Technical Notes
* References and External Links

## Notes

Much of its content was originally in the game’s Wikipedia article.