On the Regress to Infinity Backwards Being Still Impossible

The creationist arguments and its variants rely on supposing that an infinite regression is impossible. I wonder, why precisely is such an infinite series held to be impossible.

It is actually the argument of St Thomas Aquinas. As in The Five Ways. Furthermore, it is not per se Young Earth Creationist.

If one places two mirrors facing each other, there is one mirror the image of the other, which contains its own image, which contains the image of the other, which contains its own image, et cetera ad infinitum.

Has the infinitude of mirror images been truly verified? But even so, it is not an infinitude backwards in causes, but forwards in effects.

It is not infinite regression, since it regresses to the two mirrors and what is put between them as first cause, together with light, of that particular effect.

If one divides 10 by 3, the answer is 3.3333333333333, etc. ad infinitum.

The value of pi, is held to be 3.14159, etc., etc.

If become aware that I think, I think that I think, and I think that I think that I think, etc. ad infinitum.

Are each of these not infinite regressions?

If one divides 10 by 3 one gets 3 and 1/3. If one uses duodecimals, that has a finite expression: the third length of ten feet is three feet and four inches. However, a seventh would be as impossible to express in duodecimals as in decimal fractions.

Since decimal fractions are not thirds, they are incommensurable with the third, and expressing the third in decimals becomes potentially infinite - i e whenever the mathematician gives up, he knows he could theoretically go on. And that however far he went on, he would not have exactly expressed that other ratio, as he exactly expresses it by saying 3 and 1/3.

That infinitude is precisely because it is impossible to express thirds in terms of decimals - unlike halves, fourths, fifths, twentyfifths, twentieths and so on.

Similarily the relation between periphery and diameter of a true circle is irrational, because these two have no common measure. It is therefore as impossible to express in either decimals or any other fractions as are into decimals those fractions of nominators including factors other than two or five.

If the universe itself contains these infinite regressions, why should there not be an infinite regression of causes?

Neither in double mirrors, nor in decimals do we find a regress into the infinite backwards in causation.

In the case of expressing thirds, sevenths, et c. in decimal fractions or of expressing irrational geometric relations in any kind of fraction (but you can say of any decimal acquired that it is below or above the value that cannot be expressed, as you can say of any non-decimal fraction in the case of irrational relations.

Such infinitude is purely accidental, and in the effect of expressing improperly, not in causation.

In the case of double mirrors, you have just maybe an infinitude forwards in effect (not really, I think), but certainly not backward in causation.

Hans-Georg Lundahl
UL of Nanterre,
Tuesday Holy Week
(Latin and Uniate Cal.)
Year of Our Lord MMXII.

What are fractions?

Found on internet:

Sometimes the part of math that some homeschoolers have difficulty with is when it comes to working with fractions.

Now, I think the difficulty comes from not understanding what fractions are. A simplified way is to say that fractions are like portions, like the 1/8 slices of a pizza. It would be better to say that that is a particular kind of fraction.

A "fraction" is a proportion. Each 1/8 slice of a pizza or any other 1/8 part or fraction is in proportion to the whole pizza (which existed as such before it was sliced) as one is to eight.

The funny thing about proportions is ...

that it does not really matter how many are involved:

Take ten pizzas, slice them to eighty slices, the slice is still one to eight compared to the pizza.

Which explains that: 10/80=1/8.

that it may just as easily by "how much" "how long" "how heavy" "how much worth" et c as how many:

Take a pizza sliced into eight slices, again. Each piece, from the moment the slice is made, even before all the eight slices are there, is and remains one eighth of the size of the whole pizza.

But add two pizza slices like the ones before - your neighbour ate only six slices. Each slice will be 1/10 of the number of slices. It is a less proportion, but it will still be same amount of pizza. But the total amount, of which it is now only 1/10, will be those two slices bigger.

That involves:

• - each slice is still 1/8 the size of the pizza it was made from
• - each slice is now 1/10 the number of slices (since those two were added)
• - each slice is a less proportion (1/10 is less than 1/8) but same amount
• - total amount is, as such, same proportion to itself (1/1) but bigger, because new total amount is 10/8 to old total amount
• - that last proportion, 10/8, simplifies into 5/4 or 1/1 and 1/4, and the amount of pizza you have is the same as if you had had a whole pizza and a quarter slice

AND the fact that I have to apologise to my readers for making them hungry by thinking of pizza while having a math lesson. I'm getting a bit hungry myself, though I have just eaten!

Back from a meal?

Good.

Each time you eat one pizza slice, the total amount of remaining slices is less, each remaining slice remains as big as it was (until you go on and eat it) AND each slice is a bigger proportion of the remainder of pizza:

• Before you eat, each slice is 1/10 of the total amount of pizza (but still 1/8 of the pizza it was made from).
• You eat one slice, each slice is now 1/9 of the total amount of pizza (but still 1/8 of the pizza it was made from).
• You eat another, each slice is now 1/8 both ways (as much of the remainder as it was originally to the whole pizza - which remains true even if you've eaten a slice from the old pizza, which is replaced by one from the new).
• Eat three slices more, each slice is now 1/5 of the remainder (but still 1/8 of the pizza it was made from). Since the proportion has risen from 1/10 to 1/5=2/10, you might think it was twice as big? Of course not. Something wrong with the logic? No: for on the other hand, you only have 5 left instead of ten, which is 1/2; so each slice is as big as it was (if you need to check it out in maths: 1/2*2 = 1/2*2/1 = 2/2 = 1/1).
• Another big bite, each slice is 1/4 of the remainder - so, as 4/8 = 1/2 the remainder equals half a pizza. (But each slice is still 1/8 of the pizza it was made from). And if I had a pay pal account, u might have been sending me money for half a pizza (which I could not use until another one sent me money for the other half), but I have not.

If on the other hand u r a parent and think I have helped your young ones over much of the year, well consider a somewhat bigger donation. (Donativo.) If you think it needs more, click on 7 artes label or look at other related subjects at my main index page.

Hans-Georg Lundahl
Paris V, Mouffetard
31 october 2009

Mathématiques et algèbre ou compréhension et utilité

Vidarebefordradt: mattelärare kämpar för att få göra nytta!

Jag fick detta bref:

Hej!

Först och främst vill jag tacka Dig för att Du besökte mina matematiska hemsidor och för att Du skrev några rader till mig eller några meningar i min gästbok. Jag ber nu om ursäkt för att jag inte svarade dig, trots att det betydde så mycket för mig. De många breven och inläggen som har skrivits av mina hemsidors besökare, har gett mig kraft att orka kämpa vidare och har gett mig en mening i tillvaron.

Jag är en arbetslös lärare sedan flera år tillbaka. Som motprestation för den arbetslöshetsersättning och aktivitetspenningen som jag fick, men huvudsakligen som tidsfördriv, gjorde jag matematisksidor på internet. Jag gjorde hemsidorna för att kunna hjälpa de som har problem i matematik, för att kunna hjälpa elever, men även för outbildade lärare som behövde stöd. Jag trodde att jag gjorde något samhällsnyttigt.

Men den senaste utvecklingen visade istället att jag begick ett brott. Jag lade även ut skrivning/övningsuppgifter på internet. Samma eller liknande matematiska uppgifter som dagligen används och har använts under de senaste hundra åren i miljontals skolor över hela världen.

För upphovsrättsintrång dömde tingsrätten mig till böter och att betala skadestånd till upphovsmännen samt även rättegångskostnader. Det har gått så långt att Kronofogden tog mina besparningar och nu även tar den största delen av den blygsamma ersättningen som jag får från försäkringskassan. Detta har lett till att jag nu lever inom den möjligaste fattigdom som finns i Sverige.

Jag har inga medel för att kunna kämpa vidare. Men jag måste. Matematik är en vetenskap. Matematik tillhör mänskligheten och inte till någon privat ägare. Även om de matematiska uppgifterna som ligger till grund för betygsättningen i hundratals skolor i Sverige, tillåts att säljas privat och i vinstsyfte av kommunanställda lärare i gymnasieskolan till köpare.

Efter domstolsbeslutet lade jag ner mina matematiksidor, men efter de ytterligare anmälningar och fordringar som jag har fått, tänker jag lägga tillbaka allt, med en förhoppning att högre rättsliga instanser befriar mig från brottanklagelsen och skulden. Jag har lagt upp matematiklexikonet på en ny hemsideadress: http://matmin.kevius.se/, därifrån kan du ladda ned hela innehållet i en zippad form. Du kan läsa kopior av rättegångshandlingar på adressen http://www.kevius.com/ .

Jag hoppas på Din hjälp. Jag är rådlös men också medellös. För att kunna anlita en advokat eller en sakkunnig går det bra att lämna ett bidrag på följande konto på SEB: 5404 - 00 108 76 (kontohavare Bruno Kevius)

Du hjälper mig även om du visar mitt brev till dina bekanta eller hänvisar till mina matematiksidor till de som behöver och önskar grundkunskaper i matematik.

Med vänliga hälsningar


Bruno Kevius

I enlighet med önskemålet lägger jag upp det här.